["2. C\u1ef1c tr\u1ecb c\u1ee7a h\u00e0m s\u1ed1 x \u2212\u221e \u22124 0 1 +\u221e x \u2212 | \u22120+ | + x\u22121 \u2212 | \u2212 | \u22120+ (x+4)3 \u22120+ | + | + f (x) \u22120+0\u22120+ f (x) T\u1eeb b\u1ea3ng bi\u1ebfn thi\u00ean ta th\u1ea5y, h\u00e0m s\u1ed1 \u0111\u00e3 cho \u0111\u1ea1t c\u1ef1c \u0111\u1ea1i t\u1ea1i m\u1ed9t \u0111i\u1ec3m duy nh\u1ea5t x = 0. V\u1eady s\u1ed1 \u0111i\u1ec3m c\u1ef1c \u0111\u1ea1i c\u1ee7a h\u00e0m s\u1ed1 \u0111\u00e3 cho l\u00e0 1. Ch\u1ecdn \u0111\u00e1p \u00e1n D \u0104 C\u00e2u 52 (C\u00e2u 26 - M\u0110 102 - BGD&\u0110T - \u0110\u1ee3t 2 - N\u0103m 2019 - 2020). Cho h\u00e0m s\u1ed1 f (x) c\u00f3 \u0111\u1ea1o h\u00e0m f (x) = x(x \u2212 1)(x + 4)3, \u2200x \u2208 R. S\u1ed1 \u0111i\u1ec3m c\u1ef1c ti\u1ec3u c\u1ee7a h\u00e0m s\u1ed1 \u0111\u00e3 cho l\u00e0 A 2. B 3. C 4. D 1. \u0253 L\u1eddi gi\u1ea3i. \uf8eex = 0 Ta c\u00f3 f (x) = 0 \u21d4 x(x \u2212 1)(x + 4)3 = 0 \u21d4 \uf8efx = 1 \uf8f0 x = \u22124. B\u1ea3ng bi\u1ebfn thi\u00ean x \u2212\u221e \u22124 0 1 +\u221e y \u22120+0\u22120+ +\u221e f (0) +\u221e y f (\u22124) f (1) D\u1ef1a v\u00e0o b\u1ea3ng bi\u1ebfn thi\u00ean ta th\u1ea5y h\u00e0m s\u1ed1 f (x) c\u00f3 hai \u0111i\u1ec3m c\u1ef1c ti\u1ec3u. Ch\u1ecdn \u0111\u00e1p \u00e1n A \u0104 C\u00e2u 53 (C\u00e2u 33 - M\u0110 103 - BGD&\u0110T - \u0110\u1ee3t 2 - N\u0103m 2019 - 2020). Cho h\u00e0m s\u1ed1 f (x) c\u00f3 \u0111\u1ea1o h\u00e0m f (x) = x(x + 1)(x \u2212 4)3, \u2200x \u2208 R. S\u1ed1 \u0111i\u1ec3m c\u1ef1c \u0111\u1ea1i c\u1ee7a h\u00e0m s\u1ed1 \u0111\u00e3 cho l\u00e0 A 2. B 3. C 4. D 1. \u0253 L\u1eddi gi\u1ea3i. \uf8eex = 0 Ta c\u00f3 f (x) = 0 \u21d4 x(x + 1)(x \u2212 4)3 = 0 \u21d4 \uf8efx = \u22121 \uf8f0 x = 4. T\u1eeb \u0111\u00f3 ta l\u1eadp \u0111\u01b0\u1ee3c b\u1ea3ng bi\u1ebfn thi\u00ean c\u1ee7a h\u00e0m s\u1ed1 f (x) nh\u01b0 sau Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t 48 S\u0110T: 0905.193.688","Ch\u01b0\u01a1ng 1. \u1ee8NG D\u1ee4NG \u0110\u1ea0O H\u00c0M \u0110\u1ec2 KH\u1ea2O S\u00c1T V\u00c0 V\u1ebc \u0110\u1ed2 TH\u1eca C\u1ee6A H\u00c0M S\u1ed0 x \u2212\u221e \u22121 0 4 +\u221e x \u2212 | \u22120+ | + x+1 \u22120+ | + | + (x\u22124)3 \u2212 | \u2212 | \u22120+ f (x) \u22120+0\u22120+ f (x) T\u1eeb b\u1ea3ng bi\u1ebfn thi\u00ean ta th\u1ea5y, h\u00e0m s\u1ed1 \u0111\u00e3 cho \u0111\u1ea1t c\u1ef1c \u0111\u1ea1i t\u1ea1i m\u1ed9t \u0111i\u1ec3m duy nh\u1ea5t x = 0. V\u1eady s\u1ed1 \u0111i\u1ec3m c\u1ef1c \u0111\u1ea1i c\u1ee7a h\u00e0m s\u1ed1 \u0111\u00e3 cho l\u00e0 1. Ch\u1ecdn \u0111\u00e1p \u00e1n D \u0104 C\u00e2u 54 (C\u00e2u 32 - M\u0110 102 - BGD&\u0110T - \u0110\u1ee3t 4 - N\u0103m 2019 - 2020). Cho h\u00e0m s\u1ed1 f (x) c\u00f3 \u0111\u1ea1o h\u00e0m f (x) = x(x + 1)(x \u2212 4)3, \u2200x \u2208 R. S\u1ed1 \u0111i\u1ec3m c\u1ef1c ti\u1ec3u c\u1ee7a h\u00e0m s\u1ed1 \u0111\u00e3 cho l\u00e0 A 4. B 3. C 1. D 2. \u0253 L\u1eddi gi\u1ea3i. \uf8eex = \u22121 Ta c\u00f3 f (x) = 0 \u21d4 \uf8efx = 0 \uf8f0 x = 4. Ta c\u00f3 b\u1ea3ng bi\u1ebfn thi\u00ean nh\u01b0 sau x \u2212\u221e \u22121 0 4 +\u221e f (x) \u22120+0\u22120+ +\u221e f (0) +\u221e f (x) f (\u22121) f (4) T\u1eeb b\u1ea3ng bi\u1ebfn thi\u00ean ta th\u1ea5y h\u00e0m s\u1ed1 \u0111\u1ea1t c\u1ef1c ti\u1ec3u t\u1ea1i 2 \u0111i\u1ec3m x = \u22121 v\u00e0 x = 4. Ch\u1ecdn \u0111\u00e1p \u00e1n D \u0104 C\u00e2u 55 (C\u00e2u 4 - \u0110MH - BGD&\u0110T - N\u0103m 2016 - 2017). Cho h\u00e0m s\u1ed1 y = f (x) x\u00e1c \u0111\u1ecbnh, li\u00ean t\u1ee5c tr\u00ean R v\u00e0 c\u00f3 b\u1ea3ng bi\u1ebfn thi\u00ean: x \u2212\u221e 0 1 +\u221e +\u221e y+ \u22120+ 0 y \u2212\u221e \u22121 Kh\u1eb3ng \u0111\u1ecbnh n\u00e0o sau \u0111\u00e2y l\u00e0 kh\u1eb3ng \u0111\u1ecbnh \u0111\u00fang? A H\u00e0m s\u1ed1 c\u00f3 \u0111\u00fang m\u1ed9t c\u1ef1c tr\u1ecb. B H\u00e0m s\u1ed1 c\u00f3 gi\u00e1 tr\u1ecb c\u1ef1c ti\u1ec3u b\u1eb1ng 1. C H\u00e0m s\u1ed1 c\u00f3 gi\u00e1 tr\u1ecb l\u1edbn nh\u1ea5t b\u1eb1ng 0 v\u00e0 gi\u00e1 tr\u1ecb nh\u1ecf nh\u1ea5t b\u1eb1ng \u22121. D H\u00e0m s\u1ed1 \u0111\u1ea1t c\u1ef1c \u0111\u1ea1i t\u1ea1i x = 0 v\u00e0 \u0111\u1ea1t c\u1ef1c ti\u1ec3u t\u1ea1i x = 1. Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t 49 S\u0110T: 0905.193.688","2. C\u1ef1c tr\u1ecb c\u1ee7a h\u00e0m s\u1ed1 \u0253 L\u1eddi gi\u1ea3i. Lo\u1ea1i A: v\u00ec h\u00e0m s\u1ed1 c\u00f3 2 c\u1ef1c tr\u1ecb. Lo\u1ea1i B: v\u00ec h\u00e0m s\u1ed1 c\u00f3 gi\u00e1 tr\u1ecb c\u1ef1c ti\u1ec3u b\u1eb1ng \u22121. Lo\u1ea1i C: v\u00ec h\u00e0m s\u1ed1 kh\u00f4ng c\u00f3 gi\u00e1 tr\u1ecb l\u1edbn nh\u1ea5t, gi\u00e1 tr\u1ecb nh\u1ecf nh\u1ea5t tr\u00ean R. Ch\u1ecdn \u0111\u00e1p \u00e1n D \u0104 C\u00e2u 56 (C\u00e2u 20 - M\u0110 103 - BGD&\u0110T - N\u0103m 2018 - 2019). Cho h\u00e0m s\u1ed1 f (x) c\u00f3 \u0111\u1ea1o h\u00e0m f (x) = x(x \u2212 1)2, \u2200x \u2208 R. S\u1ed1 \u0111i\u1ec3m c\u1ef1c tr\u1ecb c\u1ee7a h\u00e0m s\u1ed1 \u0111\u00e3 cho l\u00e0 A 2. B 0. C 1. D 3. \u0253 L\u1eddi gi\u1ea3i. \u00f1x = 0 Ta c\u00f3 f (x) = 0 \u21d4 x=1 X\u00e9t d\u1ea5u c\u1ee7a \u0111\u1ea1o h\u00e0m x \u2212\u221e 0 1 +\u221e f (x) \u22120+0+ Ta th\u1ea5y \u0111\u1ea1o h\u00e0m \u0111\u1ed5i d\u1ea5u \u0111\u00fang 1 l\u1ea7n n\u00ean h\u00e0m s\u1ed1 \u0111\u00e3 cho c\u00f3 \u0111\u00fang 1 \u0111i\u1ec3m c\u1ef1c tr\u1ecb. Ch\u1ecdn \u0111\u00e1p \u00e1n C \u0104 C\u00e2u 57 (C\u00e2u 8 - \u0110TK - BGD&\u0110T - l\u1ea7n 1 - N\u0103m 2019 - 2020). Cho h\u00e0m s\u1ed1 y = f (x) c\u00f3 b\u1ea3ng bi\u1ebfn thi\u00ean nh\u01b0 sau x \u2212\u221e 0 3 +\u221e y +0\u22120+ 2 +\u221e y \u2212\u221e \u22124 Gi\u00e1 tr\u1ecb c\u1ef1c ti\u1ec3u c\u1ee7a h\u00e0m s\u1ed1 \u0111\u00e3 cho b\u1eb1ng A 2. B 3. C 0. D \u22124. \u0253 L\u1eddi gi\u1ea3i. T\u1eeb b\u1ea3ng bi\u1ebfn thi\u00ean ta th\u1ea5y gi\u00e1 tr\u1ecb c\u1ef1c ti\u1ec3u c\u1ee7a h\u00e0m s\u1ed1 b\u1eb1ng \u22124. Ch\u1ecdn \u0111\u00e1p \u00e1n D \u0104 C\u00e2u 58 (C\u00e2u 18 - \u0110TK - BGD&\u0110T - l\u1ea7n 1 - N\u0103m 2019 - 2020). Cho h\u00e0m s\u1ed1 f (x), b\u1ea3ng x\u00e9t d\u1ea5u c\u1ee7a f (x) nh\u01b0 sau x \u2212\u221e \u22121 0 1 +\u221e f (x) +0\u22120\u22120+ S\u1ed1 \u0111i\u1ec3m c\u1ef1c tr\u1ecb c\u1ee7a h\u00e0m s\u1ed1 \u0111\u00e3 cho l\u00e0 Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t 50 S\u0110T: 0905.193.688","Ch\u01b0\u01a1ng 1. \u1ee8NG D\u1ee4NG \u0110\u1ea0O H\u00c0M \u0110\u1ec2 KH\u1ea2O S\u00c1T V\u00c0 V\u1ebc \u0110\u1ed2 TH\u1eca C\u1ee6A H\u00c0M S\u1ed0 A 0. B 2. C 1. D 3. \u0253 L\u1eddi gi\u1ea3i. T\u1eeb b\u1ea3ng x\u00e9t d\u1ea5u c\u1ee7a f (x)ta th\u1ea5y f (x)\u0111\u1ed5i d\u1ea5u 2l\u1ea7n t\u1ea1i x = \u2212 1v\u00e0 x = 1. V\u1eady s\u1ed1 \u0111i\u1ec3m c\u1ef1c tr\u1ecb c\u1ee7a h\u00e0m s\u1ed1 \u0111\u00e3 cho l\u00e0 2. Ch\u1ecdn \u0111\u00e1p \u00e1n B \u0104 C\u00e2u 59 (C\u00e2u 13 - \u0110TK - BGD&\u0110T - l\u1ea7n 2 - N\u0103m 2019 - 2020). Cho h\u00e0m s\u1ed1 f (x) c\u00f3 b\u1ea3ng bi\u1ebfn thi\u00ean nh\u01b0 sau: x \u2212\u221e \u22121 2 +\u221e f (x) +0\u22120+ 1 +\u221e f (x) \u2212\u221e \u22122 H\u00e0m s\u1ed1 \u0111\u00e3 cho \u0111\u1ea1t c\u1ef1c \u0111\u1ea1i t\u1ea1i A x = \u22122. B x = 2. C x = 1. D x = \u22121. \u0253 L\u1eddi gi\u1ea3i. D\u1ef1a v\u00e0o BBT ta th\u1ea5y h\u00e0m s\u1ed1 \u0111\u1ea1t c\u1ef1a \u0111\u1ea1i t\u1ea1i x = \u22121. Ch\u1ecdn \u0111\u00e1p \u00e1n D \u0104 C\u00e2u 60 (C\u00e2u 33 - M\u0110 101 - BGD&\u0110T - \u0110\u1ee3t 1 - N\u0103m 2019 - 2020). Cho h\u00e0m s\u1ed1 f (x) li\u00ean t\u1ee5c tr\u00ean R v\u00e0 c\u00f3 b\u1ea3ng x\u00e9t d\u1ea5u c\u1ee7a f (x) nh\u01b0 sau: x \u2212\u221e \u22121 0 1 2 +\u221e f (x) +0\u22120+ \u22120\u2212 S\u1ed1 \u0111i\u1ec3m c\u1ef1c \u0111\u1ea1i c\u1ee7a h\u00e0m s\u1ed1 \u0111\u00e3 cho l\u00e0 A 4. B 1. C 2. D 3. \u0253 L\u1eddi gi\u1ea3i. Nh\u00ecn v\u00e0o b\u1ea3ng x\u00e9t d\u1ea5u c\u1ee7a f (x) ta th\u1ea5y, h\u00e0m s\u1ed1 c\u00f3 \u0111\u1ea1o h\u00e0m \u0111\u1ed5i d\u1ea5u t\u1eeb d\u01b0\u01a1ng sang \u00e2m khi \u0111i qua x = \u22121, x = 1 v\u00e0 h\u00e0m s\u1ed1 li\u00ean t\u1ee5c tr\u00ean R. V\u1eady h\u00e0m s\u1ed1 c\u00f3 hai \u0111i\u1ec3m c\u1ef1c \u0111\u1ea1i l\u00e0 x = \u22121 v\u00e0 x = 1. Ch\u1ecdn \u0111\u00e1p \u00e1n C \u0104 C\u00e2u 61 (C\u00e2u 17 - M\u0110 104 - BGD&\u0110T - \u0110\u1ee3t 1 - N\u0103m 2019 - 2020). Cho h\u00e0m s\u1ed1 f (x) c\u00f3 b\u1ea3ng bi\u1ebfn thi\u00ean nh\u01b0 sau x \u2212\u221e \u22121 3 +\u221e y +0\u22120+ 2 +\u221e y \u2212\u221e \u22123 Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t 51 S\u0110T: 0905.193.688","2. C\u1ef1c tr\u1ecb c\u1ee7a h\u00e0m s\u1ed1 Gi\u00e1 tr\u1ecb c\u1ef1c \u0111\u1ea1i c\u1ee7a h\u00e0m s\u1ed1 \u0111\u00e3 cho b\u1eb1ng A 3. B \u22123. C \u22121. D 2. \u0253 L\u1eddi gi\u1ea3i. T\u1eeb b\u1ea3ng bi\u1ebfn thi\u00ean suy ra gi\u00e1 tr\u1ecb c\u1ef1c \u0111\u1ea1i c\u1ee7a h\u00e0m s\u1ed1 f (x) b\u1eb1ng 2. Ch\u1ecdn \u0111\u00e1p \u00e1n D \u0104 C\u00e2u 62 (C\u00e2u 34 - M\u0110 104 - BGD&\u0110T - \u0110\u1ee3t 1 - N\u0103m 2019 - 2020). Cho h\u00e0m s\u1ed1 f (x) li\u00ean t\u1ee5c tr\u00ean R v\u00e0 c\u00f3 b\u1ea3ng x\u00e9t d\u1ea5u f (x) nh\u01b0 sau x \u2212\u221e \u22122 1 2 3 +\u221e f (x) +0\u22120+ \u22120\u2212 S\u1ed1 \u0111i\u1ec3m c\u1ef1c \u0111\u1ea1i c\u1ee7a h\u00e0m s\u1ed1 \u0111\u00e3 cho l\u00e0 A 3. B 1. C 2. D 4. \u0253 L\u1eddi gi\u1ea3i. Quan s\u00e1t b\u1ea3ng x\u00e9t d\u1ea5u f (x) ta c\u00f3 f (x) \u0111\u1ed5i d\u1ea5u t\u1eeb + sang \u2212 khi \u0111i qua c\u00e1c \u0111i\u1ec3m x = \u00b12. Do h\u00e0m s\u1ed1 \u0111\u00e3 cho li\u00ean t\u1ee5c tr\u00ean n\u00ean h\u00e0m s\u1ed1 c\u00f3 2 \u0111i\u1ec3m c\u1ef1c \u0111\u1ea1i. Ch\u1ecdn \u0111\u00e1p \u00e1n C \u0104 C\u00e2u 63 (C\u00e2u 22 - M\u0110 101 - BGD&\u0110T - N\u0103m 2021 - 2022). Cho h\u00e0m s\u1ed1 y = ax4 + bx2 + c c\u00f3 \u0111\u1ed3 th\u1ecb nh\u01b0 \u0111\u01b0\u1eddng cong trong y O h\u00ecnh b\u00ean. S\u1ed1 \u0111i\u1ec3m c\u1ef1c tr\u1ecb c\u1ee7a h\u00e0m s\u1ed1 \u0111\u00e3 cho l\u00e0 A 2. B 3. C 1. D 0. x \u0253 L\u1eddi gi\u1ea3i. D\u1ef1a v\u00e0o \u0111\u1ed3 th\u1ecb ta suy ra s\u1ed1 \u0111i\u1ec3m c\u1ef1c tr\u1ecb c\u1ee7a h\u00e0m s\u1ed1 \u0111\u00e3 l\u00e0 3. Ch\u1ecdn \u0111\u00e1p \u00e1n B \u0104 C\u00e2u 64 (C\u00e2u 5 - M\u0110 103 - BGD&\u0110T - N\u0103m 2021 - 2022). Cho h\u00e0m s\u1ed1 y = ax4 + bx2 + c c\u00f3 \u0111\u1ed3 th\u1ecb l\u00e0 \u0111\u01b0\u1eddng cong trong h\u00ecnh d\u01b0\u1edbi. y Gi\u00e1 tr\u1ecb c\u1ef1c ti\u1ec3u c\u1ee7a h\u00e0m s\u1ed1 \u0111\u00e3 cho b\u1eb1ng 4 3 A 1. B 4. C \u22121. D 3. O x \u22121 1 \u0253 L\u1eddi gi\u1ea3i. D\u1ef1a v\u00e0o \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 ta th\u1ea5y gi\u00e1 tr\u1ecb c\u1ef1c ti\u1ec3u b\u1eb1ng 3. Ch\u1ecdn \u0111\u00e1p \u00e1n D Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t 52 S\u0110T: 0905.193.688","Ch\u01b0\u01a1ng 1. \u1ee8NG D\u1ee4NG \u0110\u1ea0O H\u00c0M \u0110\u1ec2 KH\u1ea2O S\u00c1T V\u00c0 V\u1ebc \u0110\u1ed2 TH\u1eca C\u1ee6A H\u00c0M S\u1ed0 \u0104 C\u00e2u 65 (C\u00e2u 10 - \u0110TN - BGD&\u0110T - N\u0103m 2016 - 2017). Bi\u1ebft M (0; 2), N (2; \u22122) l\u00e0 c\u00e1c \u0111i\u1ec3m c\u1ef1c tr\u1ecb c\u1ee7a \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 y = ax3 + bx2 + cx + d. T\u00ednh gi\u00e1 tr\u1ecb c\u1ee7a h\u00e0m s\u1ed1 t\u1ea1i x = \u22122. A y(\u22122) = 2. B y(\u22122) = 22. C y(\u22122) = 6. D y(\u22122) = \u221218. \u0253 L\u1eddi gi\u1ea3i. Ta c\u00f3 y = 3ax2 + 2bx + c. Do M (0; 2), N (2; \u22122) l\u00e0 c\u00e1c \u0111i\u1ec3m c\u1ef1c tr\u1ecb c\u1ee7a \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 n\u00ean \uf8f1y (0) = 0 \uf8f1c = 0 \uf8f1a = 1 \uf8f4\uf8f4 \uf8f4 \uf8f4\uf8f4 \uf8f4 \uf8f2\uf8f4y (2) = 0 \uf8f4\uf8f212a + 4b + c = 0 \uf8f2\uf8f4b = \u22123 \u21d4\u21d4 \uf8f4y(0) = 2 \uf8f4d = 2 \uf8f4c = 0 \uf8f4\uf8f4 \uf8f4 \uf8f4 = \u22122 \uf8f4 \uf8f4 \uf8f3y(2) \uf8f38a + 4b + 2c + d = 0 \uf8f3d = 2 . V\u1eady h\u00e0m s\u1ed1 y = x3 \u2212 3x2 + 2. Suy ra y(\u22122) = \u221218. Ch\u1ecdn \u0111\u00e1p \u00e1n D \u0104 C\u00e2u 66 (C\u00e2u 31 - \u0110TK - BGD&\u0110T - N\u0103m 2016 - 2017). T\u00ecm t\u1ea5t c\u1ea3 c\u00e1c gi\u00e1 tr\u1ecb th\u1ef1c c\u1ee7a tham s\u1ed1 m \u0111\u1ec3 h\u00e0m s\u1ed1 y = (m \u2212 1)x4 \u2212 2(m \u2212 3)x2 + 1 kh\u00f4ng c\u00f3 c\u1ef1c \u0111\u1ea1i. A 1 \u2264 m \u2264 3. B m \u2264 1. C m \u2265 1. D 1 < m \u2264 3. \u0253 L\u1eddi gi\u1ea3i. Ta c\u00f3 y = 4(m \u2212 1)x3 \u2212 4(m \u2212 3)x = 4x [(m \u2212 1)x2 \u2212 (m \u2212 3)] (1) X\u00e9t v\u1edbi m = 1: Khi \u0111\u00f3 y = 4x2 + 1 h\u00e0m s\u1ed1 kh\u00f4ng c\u00f3 c\u1ef1c \u0111\u1ea1i. V\u1eady m = 1 th\u1ecfa m\u00e3n X\u00e9t v\u1edbi m > 1: Khi \u0111\u00f3 h\u00e0m s\u1ed1 l\u00e0 h\u00e0m b\u1eadc 4 tr\u00f9ng ph\u01b0\u01a1ng v\u1edbi h\u1ec7 s\u1ed1 a > 0 \u0111\u1ec3 h\u00e0m s\u1ed1 kh\u00f4ng c\u00f3 c\u1ef1c \u0111\u1ea1i th\u00ec y = 0 ch\u1ec9 c\u00f3 m\u1ed9t nghi\u1ec7m duy nh\u1ea5t x = 0. Hay (m \u2212 1)x2 \u2212 (m \u2212 3) = 0 v\u00f4 nghi\u1ec7m ho\u1eb7c c\u00f3 nghi\u1ec7m k\u00e9p x = 0. \u21d4 x2 = m \u2212 3 v\u00f4 nghi\u1ec7m ho\u1eb7c c\u00f3 nghi\u1ec7m x = 0 \u21d4 m \u2212 3 0\u21d41<m 3 (2) m \u2212 1 m \u2212 1 (3) X\u00e9t v\u1edbi m < 1: H\u00e0m s\u1ed1 b\u1eadc 4 tr\u00f9ng ph\u01b0\u01a1ng c\u00f3 h\u1ec7 s\u1ed1 a < 0 lu\u00f4n c\u00f3 c\u1ef1c \u0111\u1ea1i K\u1ebft lu\u1eadn: T\u1eeb (1), (2), (3) ta c\u00f3 \u0111\u1ec3 h\u00e0m s\u1ed1 kh\u00f4ng c\u00f3 c\u1ef1c \u0111\u1ea1i th\u00ec 1 m 3. Ch\u1ecdn \u0111\u00e1p \u00e1n A \u0104 C\u00e2u 67 (C\u00e2u 1 - M\u0110 102 - BGD&\u0110T - N\u0103m 2016 - 2017). Cho h\u00e0m s\u1ed1 y = f (x) c\u00f3 b\u1ea3ng bi\u1ebfn thi\u00ean nh\u01b0 sau x \u2212\u221e \u22122 2 +\u221e y +0\u22120+ 3 +\u221e y \u2212\u221e 0 T\u00ecm gi\u00e1 tr\u1ecb c\u1ef1c \u0111\u1ea1i yC\u0110 v\u00e0 gi\u00e1 tr\u1ecb c\u1ef1c ti\u1ec3u yCT c\u1ee7a h\u00e0m s\u1ed1 \u0111\u00e3 cho. A yC\u0110 = 3 v\u00e0 yCT = \u22122. B yC\u0110 = 2 v\u00e0 yCT = 0. C yC\u0110 = \u22122 v\u00e0 yCT = 2. D yC\u0110 = 3 v\u00e0 yCT = 0. \u0253 L\u1eddi gi\u1ea3i. H\u00e0m s\u1ed1 \u0111\u1ea1t c\u1ef1c \u0111\u1ea1i t\u1ea1i x = \u22122, gi\u00e1 tr\u1ecb c\u1ef1c \u0111\u1ea1i yC\u0110 = 3. H\u00e0m s\u1ed1 \u0111\u1ea1t c\u1ef1c ti\u1ec3u t\u1ea1i x = 2, gi\u00e1 tr\u1ecb c\u1ef1c ti\u1ec3u yCT = 0. Ch\u1ecdn \u0111\u00e1p \u00e1n D Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t 53 S\u0110T: 0905.193.688","2. C\u1ef1c tr\u1ecb c\u1ee7a h\u00e0m s\u1ed1 \u0104 C\u00e2u 68 (C\u00e2u 14 - M\u0110 102 - BGD&\u0110T - N\u0103m 2016 - 2017). y x \u0110\u01b0\u1eddng cong \u1edf h\u00ecnh b\u00ean l\u00e0 \u0111\u1ed3 th\u1ecb c\u1ee7a h\u00e0m s\u1ed1 y = ax4 + bx2 + c O v\u1edbi a, b, c l\u00e0 c\u00e1c s\u1ed1 th\u1ef1c. M\u1ec7nh \u0111\u1ec1 n\u00e0o d\u01b0\u1edbi \u0111\u00e2y \u0111\u00fang? A Ph\u01b0\u01a1ng tr\u00ecnh y = 0 c\u00f3 \u0111\u00fang ba nghi\u1ec7m th\u1ef1c ph\u00e2n bi\u1ec7t. B Ph\u01b0\u01a1ng tr\u00ecnh y = 0 c\u00f3 \u0111\u00fang hai nghi\u1ec7m th\u1ef1c ph\u00e2n bi\u1ec7t. C Ph\u01b0\u01a1ng tr\u00ecnh y = 0 v\u00f4 nghi\u1ec7m tr\u00ean t\u1eadp s\u1ed1 th\u1ef1c. D Ph\u01b0\u01a1ng tr\u00ecnh y = 0 c\u00f3 \u0111\u00fang m\u1ed9t nghi\u1ec7m th\u1ef1c. \u0253 L\u1eddi gi\u1ea3i. D\u1ef1a v\u00e0o \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 ta th\u1ea5y h\u00e0m s\u1ed1 c\u00f3 ba \u0111i\u1ec3m c\u1ef1c tr\u1ecb. Do \u0111\u00f3 ph\u01b0\u01a1ng tr\u00ecnh y = 0 c\u00f3 ba nghi\u1ec7m th\u1ef1c ph\u00e2n bi\u1ec7t. Ch\u1ecdn \u0111\u00e1p \u00e1n A \u0104 C\u00e2u 69 (C\u00e2u 32 - M\u0110 102 - BGD&\u0110T - N\u0103m 2016 - 2017). T\u00ecm gi\u00e1 tr\u1ecb th\u1ef1c c\u1ee7a tham s\u1ed1 m \u0111\u1ec3 h\u00e0m s\u1ed1 y = 1 x3 \u2212 mx2 + (m2 \u2212 4) x + 3 \u0111\u1ea1t c\u1ef1c \u0111\u1ea1i t\u1ea1i 3 x = 3. A m = 1. B m = \u22121. C m = 5. D m = \u22127. \u0253 L\u1eddi gi\u1ea3i. Ta c\u00f3 f (x) = x2 \u2212 2mx + m2 \u2212 4. \u0110i\u1ec1u ki\u1ec7n c\u1ea7n \u0111\u1ec3 h\u00e0m s\u1ed1 \u0111\u00e3 cho \u0111\u1ea1t c\u1ef1c \u0111\u1ea1i t\u1ea1i x = 3 l\u00e0 f (3) = 0 \u21d49 \u2212 6m + m2 \u2212 4 = 0 \u21d4m2 \u2212 6m + 5 = 0 \u00f1m = 1 \u21d4 m = 5. Khi m = 1, h\u00e0m s\u1ed1 tr\u1edf th\u00e0nh f (x) = 1 x3 \u2212 x2 \u2212 3x + 3 v\u00e0 f (x) = x2 \u2212 2x \u2212 3. Ta c\u00f3 b\u1ea3ng bi\u1ebfn thi\u00ean 3 nh\u01b0 sau x \u2212\u221e \u22121 3 +\u221e y +0\u22120+ y 14 +\u221e \u2212\u221e 3 \u22126 H\u00e0m s\u1ed1 kh\u00f4ng \u0111\u1ea1t c\u1ef1c \u0111\u1ea1i t\u1ea1i x = 3. Khi m = 5, h\u00e0m s\u1ed1 tr\u1edf th\u00e0nh f (x) = 1 x3 \u2212 5x2 + 21x + 3, f (x) = x2 \u2212 10x + 21, Ta c\u00f3 b\u1ea3ng bi\u1ebfn 3 thi\u00ean nh\u01b0 sau x \u2212\u221e 3 7 +\u221e y +0\u22120+ 30 +\u221e y 58 \u2212\u221e 3 Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t 54 S\u0110T: 0905.193.688","Ch\u01b0\u01a1ng 1. \u1ee8NG D\u1ee4NG \u0110\u1ea0O H\u00c0M \u0110\u1ec2 KH\u1ea2O S\u00c1T V\u00c0 V\u1ebc \u0110\u1ed2 TH\u1eca C\u1ee6A H\u00c0M S\u1ed0 V\u1eady h\u00e0m s\u1ed1 \u0111\u1ea1t c\u1ef1c \u0111\u1ea1i t\u1ea1i x = 3. Do \u0111\u00f3 \u0111i\u1ec1u ki\u1ec7n \u0111\u1ec3 h\u00e0m s\u1ed1 \u0111\u00e3 cho \u0111\u1ea1t c\u1ef1c \u0111\u1ea1i t\u1ea1i x = 3 l\u00e0 m = 5. Ch\u1ecdn \u0111\u00e1p \u00e1n C \u0104 C\u00e2u 70 (C\u00e2u 42 - M\u0110 102 - BGD&\u0110T - N\u0103m 2016 - 2017). Cho h\u00e0m s\u1ed1 y = f (x) c\u00f3 b\u1ea3ng bi\u1ebfn thi\u00ean nh\u01b0 sau x \u2212\u221e \u22121 3 +\u221e y +0\u22120+ 5 +\u221e y \u2212\u221e 1 \u0110\u1ed3 th\u1ecb c\u1ee7a h\u00e0m s\u1ed1 y = |f (x)| c\u00f3 bao nhi\u00eau \u0111i\u1ec3m c\u1ef1c tr\u1ecb? A 4. B 2. C 3. D 5. \u0253 L\u1eddi gi\u1ea3i. - \u0110\u1ed3 th\u1ecb h\u00e0m s\u1ed1 c\u00f3 ba \u0111i\u1ec3m c\u1ef1c tr\u1ecb. Ch\u1ecdn \u0111\u00e1p \u00e1n C \u0104 C\u00e2u 71 (C\u00e2u 5 - M\u0110 103 - BGD&\u0110T - N\u0103m 2016 - 2017). Cho h\u00e0m s\u1ed1 y = f (x) c\u00f3 b\u1ea3ng bi\u1ebfn thi\u00ean nh\u01b0 sau x \u2212\u221e \u22121 2 +\u221e y +0\u22120+ 4 2 y 25 M\u1ec7nh \u0111\u1ec1 n\u00e0o d\u01b0\u1edbi \u0111\u00e2y \u0111\u00fang? B H\u00e0m s\u1ed1 \u0111\u1ea1t c\u1ef1c ti\u1ec3u t\u1ea1i x = 2. A H\u00e0m s\u1ed1 c\u00f3 b\u1ed1n \u0111i\u1ec3m c\u1ef1c tr\u1ecb. D H\u00e0m s\u1ed1 \u0111\u1ea1t c\u1ef1c ti\u1ec3u t\u1ea1i x = \u22125. C H\u00e0m s\u1ed1 kh\u00f4ng c\u00f3 c\u1ef1c \u0111\u1ea1i. \u0253 L\u1eddi gi\u1ea3i. Nh\u00ecn b\u1ea3ng bi\u1ebfn thi\u00ean ta d\u1ec5 d\u00e0ng th\u1ea5y \u0111\u01b0\u1ee3c h\u00e0m s\u1ed1 \u0111\u1ea1t c\u1ef1c ti\u1ec3u t\u1ea1i x = 2 Ch\u1ecdn \u0111\u00e1p \u00e1n B \u0104 C\u00e2u 72 (C\u00e2u 7 - M\u0110 104 - BGD&\u0110T - N\u0103m 2016 - 2017). 2x + 3 H\u00e0m s\u1ed1 y = c\u00f3 bao nhi\u00eau \u0111i\u1ec3m c\u1ef1c tr\u1ecb? x+1 A 3. B 0. C 2. D 1. \u0253 L\u1eddi gi\u1ea3i. Ta c\u00f3 y = \u2212 (x 1 1)2 < 0, v\u1edbi m\u1ecdi x = 1. + Ch\u1ecdn \u0111\u00e1p \u00e1n B \u0104 C\u00e2u 73 (C\u00e2u 36 - M\u0110 103 - BGD&\u0110T - \u0110\u1ee3t 1 - N\u0103m 2019 - 2020). Cho h\u00e0m s\u1ed1 f (x) li\u00ean t\u1ee5c tr\u00ean v\u00e0 c\u00f3 b\u1ea3ng x\u00e9t d\u1ea5u c\u1ee7a f (x) nh\u01b0 sau: Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t 55 S\u0110T: 0905.193.688","2. C\u1ef1c tr\u1ecb c\u1ee7a h\u00e0m s\u1ed1 x \u2212\u221e \u22122 1 2 3 +\u221e f (x \u2212 0 + 0 \u2212 0 + 0 + S\u1ed1 \u0111i\u1ec3m c\u1ef1c tr\u1ecb c\u1ee7a h\u00e0m s\u1ed1 \u0111\u00e3 cho l\u00e0 A 2. B 4. C 3. D 1. \u0253 L\u1eddi gi\u1ea3i. T\u1eeb b\u1ea3ng x\u00e9t d\u1ea5u c\u1ee7a f (x) , ta th\u1ea5y f (x) \u0111\u1ed5i d\u1ea5u 3 l\u1ea7n khi qua c\u00e1c \u0111i\u1ec3m x = \u00b12; x = 1. Do \u0111\u00f3 h\u00e0m s\u1ed1 \u0111\u00e3 cho c\u00f3 3 \u0111i\u1ec3m c\u1ef1c tr\u1ecb. Ch\u1ecdn \u0111\u00e1p \u00e1n C \u0104 C\u00e2u 74 (C\u00e2u 36 - M\u0110 101 - BGD&\u0110T - N\u0103m 2017 - 2018). C\u00f3 t\u1ea5t c\u1ea3 bao nhi\u00eau gi\u00e1 tr\u1ecb nguy\u00ean c\u1ee7a m \u0111\u1ec3 h\u00e0m s\u1ed1 y = x8 + (m \u2212 2)x5 \u2212 (m2 \u2212 4)x4 + 1 \u0111\u1ea1t c\u1ef1c ti\u1ec3u t\u1ea1i x = 0? A 3. B 5. C 4. D V\u00f4 s\u1ed1. \u0253 L\u1eddi gi\u1ea3i. Ta c\u00f3 y = 8x7 + 5(m \u2212 2)x4 \u2212 4(m2 \u2212 4)x3. \u0110\u1eb7t g(x) = 8x4 + 5(m \u2212 2)x \u2212 4(m2 \u2212 4). C\u00f3 2 tr\u01b0\u1eddng h\u1ee3p c\u1ea7n x\u00e9t li\u00ean quan (m2 \u2212 4): Tr\u01b0\u1eddng h\u1ee3p 1: m2 \u2212 4 = 0 \u21d4 m = \u00b12. + Khi m = 2 \u21d2 y = 8x7 \u21d2 x = 0 l\u00e0 \u0111i\u1ec3m c\u1ef1c ti\u1ec3u. + Khi m = \u22122 \u21d2 y = x4(8x4 \u2212 20) \u21d2 x = 0 kh\u00f4ng l\u00e0 \u0111i\u1ec3m c\u1ef1c ti\u1ec3u. Tr\u01b0\u1eddng h\u1ee3p 2: m2 \u2212 4 = 0 \u21d4 m = \u00b12. Khi \u0111\u00f3 x = 0 kh\u00f4ng l\u00e0 nghi\u1ec7m c\u1ee7a g(x). Ta c\u00f3 x3 \u0111\u1ed5i d\u1ea5u t\u1eeb \u2212 sang + khi qua x0 = 0, do \u0111\u00f3 y = x3 \u00b7 g(x) \u0111\u1ed5i d\u1ea5u t\u1eeb \u2212 sang + khi qua x0 = 0 \u21d4 lim g(x) > 0 \u21d4 m2 \u2212 4 < 0. x\u21920 K\u1ebft h\u1ee3p c\u00e1c tr\u01b0\u1eddng h\u1ee3p gi\u1ea3i \u0111\u01b0\u1ee3c ta nh\u1eadn m \u2208 {2; 1; 0; \u22121}. Ch\u1ecdn \u0111\u00e1p \u00e1n C \u0104 C\u00e2u 75 (C\u00e2u 50 - M\u0110 101 - BGD&\u0110T - \u0110\u1ee3t 2 - N\u0103m 2020 - 2021). Cho h\u00e0m s\u1ed1 f (x) = x4 \u2212 12x3 + 30x2 + (4 \u2212 m)x v\u1edbi m l\u00e0 tham s\u1ed1 th\u1ef1c. C\u00f3 bao nhi\u00eau tr\u1ecb nguy\u00ean c\u1ee7a m \u0111\u1ec3 h\u00e0m s\u1ed1 g(x) = f (|x|) c\u00f3 7 \u0111i\u1ec3m c\u1ef1c tr\u1ecb. A 27. B 31. C 28. D 30. \u0253 L\u1eddi gi\u1ea3i. X\u00e9t h\u00e0m s\u1ed1 f (x) = x4 \u2212 12x3 + 30x2 + (4 \u2212 m)x. T\u1eadp x\u00e1c \u0111\u1ecbnh D = R. f (x) = 4x3 \u2212 36x2 + 60x + 4 \u2212 m. H\u00e0m s\u1ed1 g(x) = f (|x|) c\u00f3 7 \u0111i\u1ec3m c\u1ef1c tr\u1ecb \u21d4 H\u00e0m s\u1ed1 f (x) c\u00f3 3 \u0111i\u1ec3m c\u1ef1c tr\u1ecb d\u01b0\u01a1ng. \u21d4 Ph\u01b0\u01a1ng tr\u00ecnh f (x) = 0 c\u00f3 3 nghi\u1ec7m d\u01b0\u01a1ng ph\u00e2n bi\u1ec7t. X\u00e9t ph\u01b0\u01a1ng tr\u00ecnh f (x) = 0 \u21d4 4x3 \u2212 36x2 + 60x + 4 = m (1). \u0110\u1eb7t h(x) = 4x3 \u2212 36x2 + 60x + 4 \u21d4 h (x) = 12x2 \u2212 72x + 60 \u21d2 h (x) = 0 \u21d4 \u00f1x = 1 x = 5. Ta c\u00f3 b\u1ea3ng bi\u1ebfn thi\u00ean Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t 56 S\u0110T: 0905.193.688","Ch\u01b0\u01a1ng 1. \u1ee8NG D\u1ee4NG \u0110\u1ea0O H\u00c0M \u0110\u1ec2 KH\u1ea2O S\u00c1T V\u00c0 V\u1ebc \u0110\u1ed2 TH\u1eca C\u1ee6A H\u00c0M S\u1ed0 x 0 1 5 +\u221e h (x) +0\u22120+ +\u221e 32 h(x) 4 \u221296 Y\u00eau c\u1ea7u b\u00e0i to\u00e1n \u21d4 (1) c\u00f3 3 nghi\u1ec7m d\u01b0\u01a1ng ph\u00e2n bi\u1ec7t khi v\u00e0 ch\u1ec9 khi \u0111\u01b0\u1eddng th\u1eb3ng y = m c\u1eaft \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 y = h(x) t\u1ea1i 3 \u0111i\u1ec3m ph\u00e2n bi\u1ec7t c\u00f3 ho\u00e0nh \u0111\u1ed9 d\u01b0\u01a1ng. D\u1ef1a v\u00e0o BBT ta c\u00f3 4 < m < 32. V\u00ec m l\u00e0 s\u1ed1 nguy\u00ean n\u00ean m \u2208 {5; 6; 7; . . . ; 31} n\u00ean c\u00f3 27 s\u1ed1 nguy\u00ean. Ch\u1ecdn \u0111\u00e1p \u00e1n A \u0104 C\u00e2u 76 (C\u00e2u 35 - M\u0110 102 - BGD&\u0110T - N\u0103m 2016 - 2017). x+m 16 Cho h\u00e0m s\u1ed1 y = (m l\u00e0 tham s\u1ed1 th\u1ef1c) th\u1ecfa m\u00e3n min y + max y = . M\u1ec7nh \u0111\u1ec1 n\u00e0o d\u01b0\u1edbi x+1 3 [1;2] [1;2] \u0111\u00e2y \u0111\u00fang? A m \u2264 0. B m > 4. C 0 < m \u2264 2. D 2 < m \u2264 4. \u0253 L\u1eddi gi\u1ea3i. x+m 1+m 2+m - Do h\u00e0m s\u1ed1 y = li\u00ean t\u1ee5c v\u00e0 \u0111\u01a1n \u0111i\u1ec7u tr\u00ean \u0111o\u1ea1n [1; 2] n\u00ean ta c\u00f3 min y+max y = + = x+1 23 [1;2] [1;2] 16 \u21d4 m = 5. 3 Ch\u1ecdn \u0111\u00e1p \u00e1n B \u0104 C\u00e2u 77 (C\u00e2u 39 - M\u0110 103 - BGD&\u0110T - N\u0103m 2016 - 2017). \u0110\u1ed3 th\u1ecb c\u1ee7a h\u00e0m s\u1ed1 y = \u2212x3 + 3x2 + 5 c\u00f3 hai \u0111i\u1ec3m c\u1ef1c tr\u1ecb A v\u00e0 B. T\u00ednh di\u1ec7n t\u00edch S c\u1ee7a tam gi\u00e1c OAB v\u1edbi O l\u00e0 g\u1ed1c t\u1ecda \u0111\u1ed9. A S = 9. B 10 C S = 5. D S = 10. S= . 3 \u0253 L\u1eddi gi\u1ea3i. Hai \u0111i\u1ec3m c\u1ef1c ti\u1ec3u v\u00e0 c\u1ef1c \u0111\u1ea1i l\u1ea7n l\u01b0\u1ee3t l\u00e0 A(0; 5) v\u00e0 B(2; 9). Di\u1ec7n t\u00edch S = 1 \u00b7 2 \u00b7 5 = 5. 2 Ch\u1ecdn \u0111\u00e1p \u00e1n C \u0104 C\u00e2u 78 (C\u00e2u 37 - M\u0110 104 - BGD&\u0110T - N\u0103m 2016 - 2017). T\u00ecm gi\u00e1 tr\u1ecb th\u1ef1c c\u1ee7a tham s\u1ed1 m \u0111\u1ec3 \u0111\u01b0\u1eddng th\u1eb3ng d : y = (2m \u2212 1)x + 3 + m vu\u00f4ng g\u00f3c v\u1edbi \u0111\u01b0\u1eddng th\u1eb3ng \u0111i qua hai \u0111i\u1ec3m c\u1ef1c tr\u1ecb c\u1ee7a \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 y = x3 \u2212 3x2 + 1. A m= 3 B 3 C m = \u22121. D 1 . m= . 2 m= . 2 4 4 \u0253 L\u1eddi gi\u1ea3i. Ph\u01b0\u01a1ng tr\u00ecnh d qua hai c\u1ef1c tr\u1ecb l\u00e0 y = \u22122x + 1. \u0110\u1ec3 d, d vu\u00f4ng g\u00f3c v\u1edbi nhau th\u00ec \u22122(2m \u2212 1) = \u22121 \u21d0\u21d2 3 m= . 4 Ch\u1ecdn \u0111\u00e1p \u00e1n B Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t 57 S\u0110T: 0905.193.688","2. C\u1ef1c tr\u1ecb c\u1ee7a h\u00e0m s\u1ed1 \u0104 C\u00e2u 79 (C\u00e2u 45 - M\u0110 104 - BGD&\u0110T - N\u0103m 2016 - 2017). T\u00ecm t\u1ea5t c\u1ea3 c\u00e1c gi\u00e1 tr\u1ecb th\u1ef1c c\u1ee7a tham s\u1ed1 m \u0111\u1ec3 \u0111\u1ed3 th\u1ecb c\u1ee7a h\u00e0m s\u1ed1 y = x3 \u2212 3mx2 + 4m3 c\u00f3 hai \u0111i\u1ec3m c\u1ef1c tr\u1ecb A v\u00e0 B sao cho tam gi\u00e1c OAB c\u00f3 di\u1ec7n t\u00edch b\u1eb1ng 4 v\u1edbi O l\u00e0 g\u1ed1c t\u1ecda \u0111\u1ed9. A m = \u2212 \u221a1 ; m = \u221a1 . B m = \u22121; m = 1. 42 42 C m = 1. D m = 0. \u0253 L\u1eddi gi\u1ea3i. Ta c\u00f3 A(0; 4m3), B(2m; 0). Suy ra OA vu\u00f4ng g\u00f3c v\u1edbi OB. Do \u0111\u00f3 S\u2206OAB = 4m4 = 4. V\u1eady m = 1; m = \u22121. Ch\u1ecdn \u0111\u00e1p \u00e1n B \u0104 C\u00e2u 80 (C\u00e2u 49 - M\u0110 103 - BGD&\u0110T - N\u0103m 2021 - 2022). C\u00f3 bao nhi\u00eau gi\u00e1 tr\u1ecb nguy\u00ean \u00e2m c\u1ee7a tham s\u1ed1 a \u0111\u1ec3 h\u00e0m s\u1ed1 y = |x4 + ax2 \u2212 8x| c\u00f3 \u0111\u00fang 3 \u0111i\u1ec3m c\u1ef1c tr\u1ecb? A 5. B 6. C 11. D 10. \u0253 L\u1eddi gi\u1ea3i. X\u00e9t g(x) = x4 + ax2 \u2212 8x. g (x) = 4x3 + 2ax \u2212 8. X\u00e9t g (x) = 0 \u21d2 4x3 + 2ax \u2212 8 = 0 \u21d4 \u2212a = 2x3 \u2212 4 = 2x2 \u2212 4 = h(x) (do x = 0 kh\u00f4ng l\u00e0 nghi\u1ec7m). xx \uf8eex = 0 g(x) = 0 \u21d4 \uf8f0 ax \u2212 8 \u21d4 \u2212a x3 \u2212 8 x2 \u2212 8 x3 + = 0 = = = k(x). xx 4 h (x) = 4x + = 0 \u21d4 x = \u22121. x2 k (x) = 2x + 8 = 0 \u21d4 x = \u221a 3 \u22124. x2 x \u2212\u221e \u221a \u22121 0 +\u221e +\u221e 3 \u22124 +\u221e +\u221e h(x) \u221a h(\u2212 3 \u22124) 6 \u2212\u221e +\u221e +\u221e +\u221e g(x) 9 \u2212\u221e \u221a k(\u2212 3 \u22124) \u0110\u1ec3 h\u00e0m s\u1ed1 y = |g(x)| c\u00f3 \u0111\u00fang 3 c\u1ef1c tr\u1ecb \u21d4 \u2212a \u2264 6 \u21d4 a \u2265 \u22126. M\u00e0 a l\u00e0 s\u1ed1 nguy\u00ean \u00e2m n\u00ean a \u2208 {\u22126; \u22125; \u22124; \u22123; \u22122; \u22121}. Ch\u1ecdn \u0111\u00e1p \u00e1n B \u0104 C\u00e2u 81 (C\u00e2u 50 - \u0110MH - BGD&\u0110T - N\u0103m 2021 - 2022). Cho h\u00e0m s\u1ed1 y = f (x) c\u00f3 \u0111\u1ea1o h\u00e0m l\u00e0 f (x) = x2 + 10x, \u2200x \u2208 R. C\u00f3 bao nhi\u00eau gi\u00e1 tr\u1ecb nguy\u00ean c\u1ee7a tham s\u1ed1 m \u0111\u1ec3 h\u00e0m s\u1ed1 y = f (x4 \u2212 8x2 + m) c\u00f3 \u0111\u00fang 9 \u0111i\u1ec3m c\u1ef1c tr\u1ecb? Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t 58 S\u0110T: 0905.193.688","Ch\u01b0\u01a1ng 1. \u1ee8NG D\u1ee4NG \u0110\u1ea0O H\u00c0M \u0110\u1ec2 KH\u1ea2O S\u00c1T V\u00c0 V\u1ebc \u0110\u1ed2 TH\u1eca C\u1ee6A H\u00c0M S\u1ed0 A 16. B 9. C 15. D 10. \u0253 L\u1eddi gi\u1ea3i. \u00f1x = 0 Ta c\u00f3 f (x) = 0 \u21d4 x = \u221210. y = 4x3 \u2212 16x \u00b7 f x4 \u2212 8x2 + m = 0 \u21d4 \u00f14x3 \u2212 16x = 0 f x4 \u2212 8x2 + m = 0 \uf8eex = 0 \uf8efx = 2 \uf8ef \u21d4 \uf8ef\uf8efx = \u22122 \uf8ef \uf8efx4 \u2212 8x2 + m = 0 \uf8f0 x4 \u2212 8x2 + m = \u221210 \uf8eex = 0 \uf8efx = 2 \uf8ef \u21d4 \uf8ef\uf8efx = \u22122 \uf8ef \uf8efm = \u2212x4 + 8x2 (1) \uf8f0 m + 10 = \u2212x4 + 8x2 (2) \u0110\u1ec3 h\u00e0m s\u1ed1 y = f (x4 \u2212 8x2 + m) c\u00f3 9 \u0111i\u1ec3m c\u1ef1c tr\u1ecb th\u00ec f (x4 \u2212 8x2 + m) = 0 ph\u1ea3i c\u00f3 6 nghi\u1ec7m ph\u00e2n bi\u1ec7t. Suy ra ph\u01b0\u01a1ng tr\u00ecnh (1) ph\u1ea3i c\u00f3 2 nghi\u1ec7m v\u00e0 ph\u01b0\u01a1ng tr\u00ecnh (2) ph\u1ea3i c\u00f3 4 nghi\u1ec7m. \u00ae\u2212m\u22650 \u00aem \u2264 0 Ta c\u00f3: \u21d4 \u21d4 \u221210 < m \u2264 0. \u2212 16 < \u2212m \u2212 10 < 0 \u2212 10 < m < 6 Do m \u2208 Z n\u00ean m \u2208 {\u22129; \u22128; . . . ; \u22121; 0}. V\u1eady c\u00f3 10 gi\u00e1 tr\u1ecb nguy\u00ean m th\u1ecfa m\u00e3n \u0111\u1ec1 b\u00e0i. Ch\u1ecdn \u0111\u00e1p \u00e1n D \u0104 C\u00e2u 82 (C\u00e2u 46 - M\u0110 101 - BGD&\u0110T - N\u0103m 2018 - 2019). Cho h\u00e0m s\u1ed1 y = f (x), b\u1ea3ng bi\u1ebfn thi\u00ean c\u1ee7a h\u00e0m s\u1ed1 f (x) nh\u01b0 sau: x \u2212\u221e \u22121 0 1 +\u221e +\u221e +\u221e f (x) 2 \u22121 \u22123 S\u1ed1 \u0111i\u1ec3m c\u1ef1c tr\u1ecb c\u1ee7a h\u00e0m s\u1ed1 y = f (x2 \u2212 2x) l\u00e0 A 9. B 3. C 7. D 5. \u0253 L\u1eddi gi\u1ea3i. Ta c\u00f3 y = 2(x \u2212 1) \u00b7 f (x2 \u2212 2x). T\u1eeb b\u1ea3ng bi\u1ebfn thi\u00ean c\u1ee7a h\u00e0m s\u1ed1 f (x), ta c\u00f3 \uf8eex = 1 \uf8eex = 1 y \u00f1x = 1 \uf8efx2 \u2212 2x = a \u2208 (\u2212\u221e; \u22121) \uf8efx2 \u2212 2x \u2212 a = 0, a \u2208 (\u2212\u221e; \u22121) (1) = 0 \u21d4 f (x2 \u2212 2x) = 0 \uf8ef \uf8ef b \u2208 (\u22121; 0) (2) c \u2208 (0; 1) (3) \u21d4 \uf8ef\uf8efx2 \u2212 2x = b \u2208 (\u22121; 0) \u21d4 \uf8ef\uf8efx2 \u2212 2x \u2212 b = 0, (4). \uf8ef \uf8ef \uf8efx2 \u2212 2x = c \u2208 (0; 1) \uf8efx2 \u2212 2x \u2212 c = 0, \uf8f0\uf8f0 x2 \u2212 2x = d \u2208 (1; +\u221e) x2 \u2212 2x \u2212 d = 0, d \u2208 (1; +\u221e) Ta c\u00f3 b\u1ea3ng bi\u1ebfn thi\u00ean c\u1ee7a h\u00e0m s\u1ed1 y = x2 \u2212 2x Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t 59 S\u0110T: 0905.193.688","2. C\u1ef1c tr\u1ecb c\u1ee7a h\u00e0m s\u1ed1 x \u2212\u221e 1 +\u221e \u2212\u221e \u22121 +\u221e y T\u1eeb b\u1ea3ng bi\u1ebfn thi\u00ean, ta th\u1ea5y ph\u01b0\u01a1ng tr\u00ecnh (1) v\u00f4 nghi\u1ec7m, c\u00e1c ph\u01b0\u01a1ng tr\u00ecnh (2), (3), (4) \u0111\u1ec1u c\u00f3 hai nghi\u1ec7m \u0111\u01a1n ph\u00e2n bi\u1ec7t kh\u00e1c 1 v\u00e0 do b, c, d \u0111\u00f4i m\u1ed9t kh\u00e1c nhau n\u00ean c\u00e1c nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh (2), (3), (4) c\u0169ng \u0111\u00f4i m\u1ed9t kh\u00e1c nhau. Do \u0111\u00f3 f (x2 \u2212 2x) = 0 c\u00f3 6 nghi\u1ec7m \u0111\u01a1n ph\u00e2n bi\u1ec7t. V\u1eady y = 0 c\u00f3 7 nghi\u1ec7m \u0111\u01a1n ph\u00e2n bi\u1ec7t, do \u0111\u00f3 s\u1ed1 \u0111i\u1ec3m c\u1ef1c tr\u1ecb c\u1ee7a h\u00e0m s\u1ed1 y = f (x2 \u2212 2x) l\u00e0 7. Ch\u1ecdn \u0111\u00e1p \u00e1n C \u0104 C\u00e2u 83 (C\u00e2u 48 - M\u0110 102 - BGD&\u0110T - N\u0103m 2018 - 2019). Cho h\u00e0m s\u1ed1 f (x), b\u1ea3ng bi\u1ebfn thi\u00ean c\u1ee7a h\u00e0m s\u1ed1 f (x) nh\u01b0 h\u00ecnh v\u1ebd b\u00ean d\u01b0\u1edbi x \u2212\u221e \u22121 0 1 +\u221e +\u221e 2 +\u221e f (x) \u22123 \u22121 S\u1ed1 \u0111i\u1ec3m c\u1ef1c tr\u1ecb c\u1ee7a h\u00e0m s\u1ed1 y = f (x2 + 2x) l\u00e0 A 3. B 9. C 5. D 7. \u0253 L\u1eddi gi\u1ea3i. \uf8ee2x + 2 = 0 \uf8efx2 + 2x = a, a < \u22121 \uf8ef \u22121<b<0 0<c<1 Ta c\u00f3 y = (2x + 2)f (x2 + 2x) = 0 \u21d4 \uf8ef\uf8efx2 + 2x = b, d > 1. \uf8ef \uf8efx2 + 2x = c, \uf8f0 x2 + 2x = d, X\u00e9t h\u00e0m s\u1ed1 g(x) = x2 + 2x x\u00e1c \u0111\u1ecbnh tr\u00ean R, c\u00f3 y = 2x + 2, ta c\u00f3 b\u1ea3ng bi\u1ebfn thi\u00ean nh\u01b0 h\u00ecnh v\u1ebd. x \u2212\u221e \u22121 +\u221e g (x) \u22120+ +\u221e +\u221e g(x) \u22121 D\u1ef1a v\u00e0o b\u1ea3ng bi\u1ebfn thi\u00ean ta \u0111\u01b0\u1ee3c y = 0 c\u00f3 7 nghi\u1ec7m \u0111\u01a1n n\u00ean h\u00e0m s\u1ed1 \u0111\u00e3 cho c\u00f3 7 \u0111i\u1ec3m c\u1ef1c tr\u1ecb. Ch\u1ecdn \u0111\u00e1p \u00e1n D \u0104 C\u00e2u 84 (C\u00e2u 48 - M\u0110 103 - BGD&\u0110T - N\u0103m 2018 - 2019). Cho h\u00e0m s\u1ed1 f (x), b\u1ea3ng bi\u1ebfn thi\u00ean c\u1ee7a h\u00e0m s\u1ed1 f (x) nh\u01b0 sau: Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t 60 S\u0110T: 0905.193.688","Ch\u01b0\u01a1ng 1. \u1ee8NG D\u1ee4NG \u0110\u1ea0O H\u00c0M \u0110\u1ec2 KH\u1ea2O S\u00c1T V\u00c0 V\u1ebc \u0110\u1ed2 TH\u1eca C\u1ee6A H\u00c0M S\u1ed0 x \u2212\u221e \u22121 0 1 +\u221e +\u221e 2 +\u221e f (x) \u22123 \u22121 S\u1ed1 c\u1ef1c tr\u1ecb c\u1ee7a h\u00e0m s\u1ed1 y = f (4x2 \u2212 4x) l\u00e0 A 9. B 5. C 7. D 3. \u0253 L\u1eddi gi\u1ea3i. T\u1eeb b\u1ea3ng bi\u1ebfn thi\u00ean x \u2212\u221e \u22121 0 1 +\u221e +\u221e 2 +\u221e f (x) \u22123 \u22121 \uf8eex = a \u2208 (\u2212\u221e; \u22121) \uf8efx = b \u2208 (\u22121; 0) Ta th\u1ea5y f (x) = 0 \u21d4 \uf8ef \uf8f0\uf8efx = c \u2208 (0; 1) x = d \u2208 (1; +\u221e). V\u1edbi y = f (4x2 \u2212 4x), ta c\u00f3 y = (8x \u2212 4)f (4x2 \u2212 4x) \uf8ee1 x= 2 \uf8ef \u00f18x \u2212 4 = 0 \uf8ef4x2 \u2212 4x = a \u2208 (\u2212\u221e; \u22121)(1) \uf8ef y =0\u21d4 f (4x2 \u2212 4x) = 0 \u21d4 \uf8ef\uf8ef4x2 \u2212 4x = b \u2208 (\u22121; 0)(2) \uf8ef \uf8f0\uf8ef4x2 \u2212 4x = c \u2208 (0; 1)(3) . 4x2 \u2212 4x = d \u2208 (1; +\u221e)(4) X\u00e9t h\u00e0m s\u1ed1 g(x) = 4x2 \u2212 4x, ta c\u00f3 g (x) = 8x \u2212 4 = 0 \u21d4 x = 1 2 B\u1ea3ng bi\u1ebfn thi\u00ean x \u2212\u221e 1 +\u221e 2 g (x) \u22120+ +\u221e +\u221e g(x) \u22121 T\u1eeb b\u1ea3ng bi\u1ebfn thi\u00ean c\u1ee7a g(x) ta c\u00f3 V\u00ec a \u2208 (\u2212\u221e; \u22121) n\u00ean (1) v\u00f4 nghi\u1ec7m. V\u00ec b \u2208 (\u22121; 0) n\u00ean (2) c\u00f3 2 nghi\u1ec7m ph\u00e2n bi\u1ec7t. V\u00ec c \u2208 (0; 1) n\u00ean (3) c\u00f3 2 nghi\u1ec7m ph\u00e2n bi\u1ec7t. V\u00ec d \u2208 (1; +\u221e) n\u00ean (4) c\u00f3 2 nghi\u1ec7m ph\u00e2n bi\u1ec7t. Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t 61 S\u0110T: 0905.193.688","2. C\u1ef1c tr\u1ecb c\u1ee7a h\u00e0m s\u1ed1 V\u1eady h\u00e0m s\u1ed1 y = f (4x2 \u2212 4x) c\u00f3 7 \u0111i\u1ec3m c\u1ef1c tr\u1ecb C\u00e1ch kh\u00e1c Ta c\u00f3: y = (8x \u2212 4) \u00b7 f (4x2 \u2212 4x). y = 0 \u21d4 (8x \u2212 4) \u00b7 f (4x2 \u2212 4x) = 0 \u21d4 \u00f18x \u2212 4 = 0 = 0. f (4x2 \u2212 4x) 8x \u2212 4 = 0 \u21d4 x = 1 . 2 \uf8ee4x2 \u2212 4x = a (a < \u22121) (1) f (4x2 \u2212 4x) = 0 \u21d4 \uf8ef4x2 \u2212 4x = b (\u22121 < b < 0) (2) \uf8ef \u2212 4x = c (0 < c < 1) (3) \uf8f0\uf8ef4x2 4x2 \u2212 4x = d (d > 1) (4). Ph\u01b0\u01a1ng tr\u00ecnh 4x2 \u2212 4x = m \u21d4 4x2 \u2212 4x \u2212 m = 0 c\u00f3 nghi\u1ec7m khi \u2206 = 4 \u2212 4m \u2265 0 hay m \u2264 1. T\u1eeb \u0111\u00f3, ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh (1); (2); (3) lu\u00f4n c\u00f3 hai nghi\u1ec7m ph\u00e2n bi\u1ec7t. Ph\u01b0\u01a1ng tr\u00ecnh (4) v\u00f4 nghi\u1ec7m. Do \u0111\u00f3, h\u00e0m s\u1ed1 \u0111\u00e3 cho c\u00f3 7 c\u1ef1c tr\u1ecb. Ch\u1ecdn \u0111\u00e1p \u00e1n C \u0104 C\u00e2u 85 (C\u00e2u 50 - M\u0110 104 - BGD&\u0110T - N\u0103m 2018 - 2019). Cho h\u00e0m s\u1ed1 f (x), b\u1ea3ng bi\u1ebfn thi\u00ean c\u1ee7a h\u00e0m s\u1ed1 f (x) nh\u01b0 sau: x \u2212\u221e \u22121 0 1 +\u221e +\u221e 2 +\u221e f (x) \u22123 \u22121 S\u1ed1 \u0111i\u1ec3m c\u1ef1c tr\u1ecb c\u1ee7a h\u00e0m s\u1ed1 y = f (4x2 + 4x) l\u00e0 A 5. B 9. C 7. D 3. \u0253 L\u1eddi gi\u1ea3i. C\u00f3 (f (4x2 + 4x)) = (8x + 4)f (4x2 + 4x), (f (4x2 + 4x)) = 0 \u21d4 \uf8ee = \u2212 1 2 x \uf8f0 f (4x2 + 4x) = 0. B\u1ea3ng bi\u1ebfn thi\u00ean x \u2212\u221e \u22121 0 1 +\u221e +\u221e 2 +\u221e f (x) a1 a2 a3 a4 \u22123 \u22121 \uf8ee4x2 + 4x = a1 \u2208 (\u2212\u221e; \u22121) T\u1eeb b\u1ea3ng bi\u1ebfn thi\u00ean tr\u00ean ta c\u00f3 f (4x2 + 4x) = 0 \u21d4 \uf8ef4x2 + 4x = a2 \u2208 (\u22121; 0) . (1) \uf8ef + 4x = a3 \u2208 (0; 1) \uf8ef\uf8f04x2 4x2 + 4x = a4 \u2208 (1; +\u221e) X\u00e9t g(x) = 4x2 + 4x, g (x) = 8x + 4, g (x) = 0 \u21d4 x = \u2212 1 ta c\u00f3 b\u1ea3ng bi\u1ebfn thi\u00ean 2 Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t 62 S\u0110T: 0905.193.688","Ch\u01b0\u01a1ng 1. \u1ee8NG D\u1ee4NG \u0110\u1ea0O H\u00c0M \u0110\u1ec2 KH\u1ea2O S\u00c1T V\u00c0 V\u1ebc \u0110\u1ed2 TH\u1eca C\u1ee6A H\u00c0M S\u1ed0 x \u2212\u221e \u22121 +\u221e 2 g (x) \u22120+ +\u221e +\u221e g(x) 1 K\u1ebft h\u1ee3p b\u1ea3ng bi\u1ebfn thi\u00ean c\u1ee7a g(x) v\u00e0 h\u1ec7 (1) ta th\u1ea5y: Ph\u01b0\u01a1ng tr\u00ecnh 4x2 + 4x = a1 \u2208 (\u2212\u221e; \u22121) v\u00f4 nghi\u1ec7m. Ph\u01b0\u01a1ng tr\u00ecnh 4x2 + 4x = a2 \u2208 (\u22121; 0) t\u00ecm \u0111\u01b0\u1ee3c hai nghi\u1ec7m ph\u00e2n bi\u1ec7t kh\u00e1c \u22121. 2 Ph\u01b0\u01a1ng tr\u00ecnh 4x2 + 4x = a2 \u2208 (0; 1) t\u00ecm \u0111\u01b0\u1ee3c th\u00eam hai nghi\u1ec7m m\u1edbi ph\u00e2n bi\u1ec7t kh\u00e1c \u22121. 2 Ph\u01b0\u01a1ng tr\u00ecnh 4x2 + 4x = a2 \u2208 (1; +\u221e) t\u00ecm \u0111\u01b0\u1ee3c th\u00eam hai nghi\u1ec7m ph\u00e2n bi\u1ec7t kh\u00e1c \u22121. 2 V\u1eady h\u00e0m s\u1ed1 y = f (4x2 + 4x) c\u00f3 t\u1ea5t c\u1ea3 7 \u0111i\u1ec3m c\u1ef1c tr\u1ecb. Ch\u1ecdn \u0111\u00e1p \u00e1n C \u0104 C\u00e2u 86 (C\u00e2u 46 - \u0110TK - BGD&\u0110T - l\u1ea7n 1 - N\u0103m 2019 - 2020). Cho h\u00e0m s\u1ed1 b\u1eadc b\u1ed1n y = f (x) c\u00f3 \u0111\u1ed3 th\u1ecb nh\u01b0 h\u00ecnh b\u00ean . S\u1ed1 \u0111i\u1ec3m c\u1ef1c y 4x tr\u1ecb c\u1ee7a h\u00e0m s\u1ed1 g(x) = f (x3 + 3x2) l\u00e0 O A 5. B 3. C 7. D 11. \u0253 L\u1eddi gi\u1ea3i. \uf8eex = a \u2208 (\u2212\u221e; 0) D\u1ef1a v\u00e0o \u0111\u1ed3 th\u1ecb y = f (x)ta c\u00f3: f (x) = 0 \u21d4 \uf8efx = b \u2208 (0; 4) \uf8f0 x = c \u2208 (4 ; +\u221e) Ta c\u00f3: g (x) = (3x2 + 6x) f (x3 + 3x2). \uf8eex = 0 g (x) = 0 \u21d4 \u00f13x2 + 6x = 0 = 0 \u21d4 \uf8efx = \u22122 = a \u2208 (\u2212\u221e; 0) (1) . f x3 + 3x2 \uf8ef = b \u2208 (0; 4) (2) (3) \uf8ef\uf8efx3 + 3x2 \uf8ef \uf8efx3 + 3x2 \uf8f0 x3 + 3x2 = c \u2208 (4; +\u221e) X\u00e9t h\u00e0m s\u1ed1 : h(x) = x3 + 3x2 Ta c\u00f3 h (x) = 3x2 + 6x,h (x) = 0 \u21d4 3x2 + 6x = 0 \u21d4 \u00f1x = 0 . x = \u22122 B\u1ea3ng bi\u1ebfn thi\u00ean Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t 63 S\u0110T: 0905.193.688","2. C\u1ef1c tr\u1ecb c\u1ee7a h\u00e0m s\u1ed1 x \u2212\u221e \u22122 0 +\u221e y +0\u22120+ 4 +\u221e y \u2212\u221e 0 D\u1ef1a v\u00e0o b\u1ea3ng bi\u1ebfn thi\u00ean ta c\u00f3 Ph\u01b0\u01a1ng tr\u00ecnh (1)c\u00f3 m\u1ed9t nghi\u1ec7m . Ph\u01b0\u01a1ng tr\u00ecnh (2)c\u00f3 ba nghi\u1ec7m ph\u00e2n bi\u1ec7t . Ph\u01b0\u01a1ng tr\u00ecnh (3)c\u00f3 m\u1ed9t nghi\u1ec7m . V\u1eady ph\u01b0\u01a1ng tr\u00ecnh g (x) = 0 c\u00f3 7 nghi\u1ec7m b\u1ed9i l\u1ebb ph\u00e2n bi\u1ec7t n\u00ean h\u00e0m s\u1ed1 c\u00f3 7 \u0111i\u1ec3m c\u1ef1c tr\u1ecb. Ch\u1ecdn \u0111\u00e1p \u00e1n C \u0104 C\u00e2u 87 (C\u00e2u 44 - M\u0110 101 - BGD&\u0110T - \u0110\u1ee3t 1 - N\u0103m 2019 - 2020). Cho h\u00e0m s\u1ed1 b\u1eadc b\u1ed1n f (x) c\u00f3 b\u1ea3ng bi\u1ebfn thi\u00ean nh\u01b0 sau: x \u2212\u221e \u22121 0 1 +\u221e y \u22120+0\u22120+ +\u221e 3 +\u221e y \u22122 \u22122 S\u1ed1 \u0111i\u1ec3m c\u1ef1c tr\u1ecb c\u1ee7a h\u00e0m s\u1ed1 g(x) = x4 [f (x + 1)]2 l\u00e0 A 11. B 9. C 7. D 5. \u0253 L\u1eddi gi\u1ea3i. C\u00e1ch 1. V\u00ec f (x) l\u00e0 h\u00e0m b\u1eadc b\u1ed1n n\u00ean f (x) l\u00e0 h\u00e0m b\u1eadc ba c\u00f3 h\u1ec7 s\u1ed1 b\u1eadc ba \u0111\u1ed3ng th\u1eddi nh\u1eadn c\u00e1c gi\u00e1 tr\u1ecb \u22121; 0; 1 l\u00e0m nghi\u1ec7m. Do \u0111\u00f3 f (x) = ax (x \u2212 1) (x + 1) = a x3 \u2212 x \u21d2 f (x) = \u00c5 x4 \u2212 x2 \u00e3 + b a 42 V\u00ec f (0) = 3 v\u00e0 f (1) = \u22122 n\u00ean suy ra a = 20; b = 3. V\u1eady f (x) = 5x4 \u2212 10x2 + 3 = 5 (x2 \u2212 1)2 \u2212 2, suy ra f (x + 1) = 5 (x2 + 2x)2 \u2212 2. Ta c\u00f3 g (x) = [x2 \u00b7 f (x + 1)]2 = \u00ee5x2 (x2 + 2x)2 \u2212 2x2\u00f32. 5x2 x2 + 2x 2 = 2x2 (1) (2) g (x) = 0 \u21d4 10x x2 + 2x 2 + 10x2 x2 + 2x (2x + 2) = 4x \uf8eex = 0 nghi\u1ec7m k\u00e9p \uf8eex = 0 Ph\u01b0\u01a1ng tr\u00ecnh (1) \u21d4 \uf8ef + 2x = \u20262 \uf8efx \u2248 0, 277676 \uf8ef\uf8efx2 5 \uf8ef \uf8ef \u21d4 \uf8ef\uf8efx \u2248 \u22122, 277676. \uf8ef + 2x = \u2026 2 \uf8ef \uf8f0 \u2212 \uf8efx \u2248 \u22120, 393746 5 \uf8f0 x2 x \u2248 \u22121, 606254 \uf8eex = 0 Ph\u01b0\u01a1ng tr\u00ecnh (2) \u21d4 \u00f1x = 0 50x3 + 40x2 \u2212 2 = 0 \u21d4 \uf8efx \u2248 \u22122, 0448 15x4 + \uf8ef \u2248 \u22121, 21842. \uf8ef\uf8efx \uf8ef \uf8efx \u2248 \u22120, 26902 \uf8f0 x \u2248 0, 19893 Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t 64 S\u0110T: 0905.193.688","Ch\u01b0\u01a1ng 1. \u1ee8NG D\u1ee4NG \u0110\u1ea0O H\u00c0M \u0110\u1ec2 KH\u1ea2O S\u00c1T V\u00c0 V\u1ebc \u0110\u1ed2 TH\u1eca C\u1ee6A H\u00c0M S\u1ed0 So s\u00e1nh c\u00e1c nghi\u1ec7m gi\u1ea3i b\u1eb1ng m\u00e1y t\u00ednh c\u1ea7m tay ta c\u00f3 9 nghi\u1ec7m kh\u00f4ng tr\u00f9ng nhau, trong \u0111\u00f3 8 nghi\u1ec7m \u0111\u01a1n v\u00e0 nghi\u1ec7m x = 0 l\u00e0 nghi\u1ec7m b\u1ed9i 3 n\u00ean g (x) c\u00f3 9 \u0111i\u1ec3m c\u1ef1c tr\u1ecb. V\u1eady g (x) c\u00f3 9 \u0111i\u1ec3m c\u1ef1c tr\u1ecb. C\u00e1ch 2. T\u1eeb b\u1ea3ng bi\u1ebfn thi\u00ean ta th\u1ea5y r\u1eb1ng ph\u01b0\u01a1ng tr\u00ecnh f (x) = 0 c\u00f3 4 nghi\u1ec7m ph\u00e2n bi\u1ec7t. H\u00e0m s\u1ed1 g(x) x\u00e1c \u0111\u1ecbnh v\u00e0 li\u00ean t\u1ee5c tr\u00ean R, c\u00f3 g (x) = 4x3 [f (x + 1)]2 + 2x4f (x + 1) \u00b7 f (x + 1) (*) = 2x3f (x + 1) [2f (x + 1) + xf (x + 1)] Ta th\u1ea5y r\u1eb1ng h\u00e0m f (x) b\u1eadc 4 n\u00ean h\u00e0m g(x) c\u00f3 t\u1ed1i \u0111a 9 \u0111i\u1ec3m c\u1ef1c tr\u1ecb. M\u1eb7t kh\u00e1c ph\u01b0\u01a1ng tr\u00ecnh g(x) = 0 c\u00f3 t\u1ea5t c\u1ea3 5 nghi\u1ec7m b\u1ed9i ch\u1eb5n, n\u00ean \u0111\u1ed3 th\u1ecb h\u00e0m g(x) s\u1ebd c\u00f3 d\u1ea1ng x Nh\u01b0 v\u1eady h\u00e0m s\u1ed1 \u0111\u00e3 cho c\u00f3 t\u1ea5t c\u1ea3 9 \u0111i\u1ec3m c\u1ef1c tr\u1ecb. Ch\u1ecdn \u0111\u00e1p \u00e1n B \u0104 C\u00e2u 88 (C\u00e2u 45 - M\u0110 102 - BGD&\u0110T - \u0110\u1ee3t 1 - N\u0103m 2019 - 2020). Cho h\u00e0m s\u1ed1 b\u1eadc b\u1ed1n f (x) c\u00f3 b\u1ea3ng bi\u1ebfn thi\u00ean nh\u01b0 sau: x \u2212\u221e \u22121 0 1 +\u221e f (x) +0\u22120+0\u2212 33 f (x) \u2212\u221e \u22121 \u2212\u221e S\u1ed1 \u0111i\u1ec3m c\u1ef1c tr\u1ecb c\u1ee7a h\u00e0m s\u1ed1 g(x) = x2 [f (x \u2212 1)]4 l\u00e0 A 7. B 8. C 5. D 9. \u0253 L\u1eddi gi\u1ea3i. T\u1eeb b\u1ea3ng bi\u1ebfn thi\u00ean ta th\u1ea5y f (x) = a(x2 \u2212 1)x = ax3 \u2212 ax \u21d2 f (x) = ax4 \u2212 ax2 + c. 42 \u0110\u1ed3 th\u1ecb h\u00e0m s\u1ed1 \u0111i qua \u0111i\u1ec3m (0; \u22121) n\u00ean c = \u22121. \u0110i\u1ec3m (1; 3) thu\u1ed9c \u0111\u1ed3 th\u1ecb n\u00ean c\u00f3 a \u2212 a \u2212 1 = 3 \u21d2 a = \u221216. 42 Ta c\u00f3 h\u00e0m s\u1ed1 f (x) = \u22124x4 + 8x2 \u2212 1, f (x) = \u221216x(x2 \u2212 1). \u0110\u1eb7t t = x \u2212 1 \u21d2 x = t + 1 ta c\u00f3 h\u00e0m s\u1ed1 g(t + 1) = (t + 1)2 [f (t)]4. g (t + 1) = 2(t + 1)[f (t)]4 + 4(t + 1)2 [f (t)]3 f (t)=2(t + 1)[f (t)]3 [f (t) + 2(t + 1)f (t)]. \uf8f1t = \u22121 \uf8f4 \uf8f2 g (t + 1) = 0 \u21d4 f (t) = 0 \uf8f4\uf8f3f (t) + 2(t + 1)f (t) = 0. + Ph\u01b0\u01a1ng tr\u00ecnh f (t) + 2(t + 1)f (t) = 0 \u21d4 \u22124t4 + 8t2 \u2212 1 + 2(t + 1)(\u221216)t(t2 \u2212 1) = 0 \u21d4 \u221236t4 \u2212 32t3 + 40t2 + 32t \u2212 1 = 0. Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t 65 S\u0110T: 0905.193.688","2. C\u1ef1c tr\u1ecb c\u1ee7a h\u00e0m s\u1ed1 X\u00e9t v\u1ebf tr\u00e1i: h(t) = \u221236t4 \u2212 32t3 + 40t2 + 32t \u2212 1. h (t) = \u2212144t3 \u2212 96t2 + 80t + 32 = \u2212144(t + 1) \u00c5 + 1\u00e3 \u00c5 \u2212 2\u00e3 t t . 33 t \u2212\u221e \u22121 \u22121 2 +\u221e 3 3 f (t) + 0 \u2212 0 + 0 \u2212 f (t) 3 581 \u2212\u221e 27 \u2212 175 \u2212\u221e 27 T\u1eeb \u0111\u00e2y suy ra ph\u01b0\u01a1ng tr\u00ecnh h(t) = 0 c\u00f3 4 nghi\u1ec7m ph\u00e2n bi\u1ec7t. + Ph\u01b0\u01a1ng tr\u00ecnh f (t) = 0 c\u00f3 4 nghi\u1ec7m ph\u00e2n bi\u1ec7t. V\u1eady ph\u01b0\u01a1ng tr\u00ecnh g (t + 1) = 0 c\u00f3 9 nghi\u1ec7m ph\u00e2n bi\u1ec7t n\u00ean h\u00e0m s\u1ed1 g(x) = x2 [f (x \u2212 1)]4 c\u00f3 9 \u0111i\u1ec3m c\u1ef1c tr\u1ecb. Ch\u1ecdn \u0111\u00e1p \u00e1n D \u0104 C\u00e2u 89 (C\u00e2u 46 - M\u0110 104 - BGD&\u0110T - \u0110\u1ee3t 1 - N\u0103m 2019 - 2020). Cho h\u00e0m s\u1ed1 b\u1eadc b\u1ed1n f (x) c\u00f3 b\u1ea3ng bi\u1ebfn thi\u00ean sau: x \u2212\u221e \u22121 0 1 +\u221e y +0\u22120+0\u2212 3 3 y \u2212\u221e \u22122 \u2212\u221e S\u1ed1 \u0111i\u1ec3m c\u1ef1c tr\u1ecb c\u1ee7a h\u00e0m s\u1ed1 g (x) = x2 [f (x + 1)]4 l\u00e0 A 7. B 8. C 5. . D 9. \u0253 L\u1eddi gi\u1ea3i. D\u1ef1a v\u00e0o b\u1ea3ng bi\u1ebfn thi\u00ean, x\u00e9t f (x) = ax4 + bx2 + c \u21d2 f (x) = 4ax3 + 2bx \uf8f1a + b + c = 3 \uf8f1a = \u22125 \uf8f4\uf8f4 \uf8f2\uf8f2 C\u0169ng theo BBT ta c\u00f3 f (\u22121) = 3; f (0) = \u22122; f (1) = 0 \u21d2 c = \u22122 \u21d4 b = 10 . \uf8f3\uf8f44a + 2b = 0 \uf8f4\uf8f3c = \u22122 \u21d2 f (x) = \u22125x4 +10x2 \u22122. \u0110\u1eb7t X = x\u22121 \u21d2 x = X +1 khi \u0111\u00f3 g (X) = (X + 1)2 (\u22125X4 + 10X2 \u2212 2)4. \u21d2 g (X) = 2 (X + 1) (\u22125X4 + 10X2 \u2212 2)4 + 4 (X + 1)2 (\u221220X3 + 20X) (\u22125X4 + 10X2 \u2212 2)3 = 2 (X + 1) (\u22125X4 + 10X2 \u2212 2)3 (\u221245X4 \u2212 40X3 + 50X2 + 40X \u2212 2) \uf8eeX + 1 = 0 \u21d2 g (X) = 0 \u21d4 \uf8ef \u2212 5X4 + 10X2 \u2212 2 = 0 \uf8f0 \u2212 45X4 \u2212 40X3 + 50X2 + 40X \u2212 2 +) V\u1edbi X = \u22121 \u21d2 x = 0 (nghi\u1ec7m b\u1ed9i l\u1ebb). (1) \u221a \uf8ee 5 + 15 t= >0 5\u221a . +) V\u1edbi \u22125X 4 + 10X 2 \u2212 2 = 0. \u0110\u1eb7t t = X2, (t \u2265 0) \u21d2 \u22125t2 + 10t \u2212 2 = 0 \u21d4 \uf8ef \uf8ef \uf8f0 5 \u2212 15 t= >0 5 \u21d2 \u22125X4 + 10X2 \u2212 2 = 0 c\u00f3 4 nghi\u1ec7m X n\u00ean c\u00f3 4 nghi\u1ec7m x (nghi\u1ec7m b\u1ed9i l\u1ebb). (2) +) X\u00e9t f (X) = \u221245X4 \u2212 40X3 + 50X2 + 40X \u2212 2 Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t 66 S\u0110T: 0905.193.688","Ch\u01b0\u01a1ng 1. \u1ee8NG D\u1ee4NG \u0110\u1ea0O H\u00c0M \u0110\u1ec2 KH\u1ea2O S\u00c1T V\u00c0 V\u1ebc \u0110\u1ed2 TH\u1eca C\u1ee6A H\u00c0M S\u1ed0 \uf8ee = \u22121 X \uf8ef3 Khi \u0111\u00f3 f (X) = \u2212180X3 \u2212 120X2 + 100X + 40 \u21d2 f (X ) = 0 \u21d4 \uf8ef = 2 . \uf8ef\uf8efX 3 \uf8f0 X = \u22121 Ta c\u00f3 B\u1ea3ng bi\u1ebfn thi\u00ean. x \u2212\u221e \u22121 \u22121 2 +\u221e 3 3 y +0\u22120+0\u2212 3 706 27 y \u2212 239 \u2212\u221e \u2212\u221e 7 D\u1ef1a v\u00e0o BBT ta c\u00f3 \u221245X4 \u2212 40X3 + 50X2 + 40X \u2212 2 = 0 c\u00f3 4 nghi\u1ec7m n\u00ean c\u0169ng c\u00f3 4 nghi\u1ec7m x (nghi\u1ec7m b\u1ed9i l\u1ebb).(3) T\u1eeb (1) , (2) , (3) ta suy ra g (x) = 0 c\u00f3 9 nghi\u1ec7m b\u1ed9i l\u1ebb v\u00e0 ph\u00e2n bi\u1ec7t n\u00ean g (x) c\u00f3 9 c\u1ef1c tr\u1ecb Ch\u1ecdn \u0111\u00e1p \u00e1n D \u0104 C\u00e2u 90 (C\u00e2u 45 - M\u0110 103 - BGD&\u0110T - \u0110\u1ee3t 2 - N\u0103m 2019 - 2020). Cho h\u00e0m s\u1ed1 f (x) c\u00f3 f (0) = 0. Bi\u1ebft y = f (x) l\u00e0 h\u00e0m s\u1ed1 b\u1eadc y y = f (x) b\u1ed1n v\u00e0 c\u00f3 \u0111\u1ed3 th\u1ecb l\u00e0 \u0111\u01b0\u1eddng cong trong h\u00ecnh b\u00ean. S\u1ed1 \u0111i\u1ec3m c\u1ef1c tr\u1ecb c\u1ee7a h\u00e0m s\u1ed1 g(x) = |f (x4) \u2212 x2| l\u00e0 A 4. B 3. C 6. D 5. Ox \u0253 L\u1eddi gi\u1ea3i. Ta c\u00f3 s\u1ed1 \u0111i\u1ec3m c\u1ef1c tr\u1ecb c\u1ee7a h\u00e0m s\u1ed1 g(x) b\u1eb1ng s\u1ed1 c\u1ef1c tr\u1ecb c\u1ee7a h\u00e0m s\u1ed1 h(x) = f (x4) \u2212 x2 c\u1ed9ng v\u1edbi s\u1ed1 giao \u0111i\u1ec3m c\u1ee7a \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 h(x) v\u1edbi tr\u1ee5c ho\u00e0nh (kh\u00f4ng t\u00ednh ti\u1ebfp x\u00fac). Ta c\u00f3 h (x) = 4x3f (x4) \u2212 2x = 2x 2x2f (x4) \u2212 1 , \u00f1x = 0 (1) h (x) = 0 \u21d4 x2f (x4) \u2212 1 = 0. V\u00ec x = 0 kh\u00f4ng ph\u1ea3i l\u00e0 nghi\u1ec7m c\u1ee7a (1) n\u00ean (1) \u21d4 f (x4) = 1 (2) . x2 \u0110\u1eb7t t = x4, t > 0. Ph\u01b0\u01a1ng tr\u00ecnh (2) tr\u1edf th\u00e0nh f (t) = \u221a1 . (3) y t y = f (t) Do v\u1edbi t > 0 th\u00ec y = f (t) l\u00e0 h\u00e0m \u0111\u1ed3ng bi\u1ebfn c\u00f2n y = \u221a1 l\u00e0 h\u00e0m y = \u221a1 t t ngh\u1ecbch bi\u1ebfn, h\u01a1n n\u1eefa lim \u221a1 = +\u221e n\u00ean d\u1ef1a v\u00e0o \u0111\u1ed3 th\u1ecb suy ra Ot t\u21920+ t ph\u01b0\u01a1ng tr\u00ecnh (3) c\u00f3 nghi\u1ec7m t0 > 0 du\u221ay nh\u1ea5t. T\u1eeb \u0111\u00f3 suy ra ph\u01b0\u01a1ng tr\u00ecnh (2) c\u00f3 hai nghi\u1ec7m ph\u00e2n bi\u1ec7t \u00b1 4 t0. Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t 67 S\u0110T: 0905.193.688","2. C\u1ef1c tr\u1ecb c\u1ee7a h\u00e0m s\u1ed1 \u221a V\u1eady h (x) = 0 c\u00f3 3 nghi\u1ec7m (\u0111\u01a1n) ph\u00e2n bi\u1ec7t x = 0 v\u00e0 x = \u00b1 4 t0. Ta c\u00f3 b\u1ea3ng bi\u1ebfn thi\u00ean c\u1ee7a h\u00e0m h(x) nh\u01b0 h\u00ecnh d\u01b0\u1edbi \u0111\u00e2y x \u2212\u221e \u221a 0 \u221a \u2212 4 t0 4 t0 +\u221e h (x) \u22120+0\u22120+ +\u221e 0 +\u221e h(x) D\u1ef1a v\u00e0o b\u1ea3ng bi\u1ebfn thi\u00ean, suy ra \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 h(x) c\u1eaft tr\u1ee5c ho\u00e0nh t\u1ea1i 2 \u0111i\u1ec3m (t\u1ea1i x = 0, \u0111\u1ed3 th\u1ecb h(x) ti\u1ebfp x\u00fac tr\u1ee5c ho\u00e0nh). V\u1eady h\u00e0m s\u1ed1 g(x) = |h(x)| c\u00f3 5 c\u1ef1c tr\u1ecb. Ch\u1ecdn \u0111\u00e1p \u00e1n D \u0104 C\u00e2u 91 (C\u00e2u 38 - M\u0110 102 - BGD&\u0110T - N\u0103m 2017 - 2018). C\u00f3 bao nhi\u00eau gi\u00e1 tr\u1ecb nguy\u00ean c\u1ee7a tham s\u1ed1 m \u0111\u1ec3 h\u00e0m s\u1ed1 y = x8 + (m \u2212 1)x5 \u2212 (m2 \u2212 1)x4 + 1 \u0111\u1ea1t c\u1ef1c ti\u1ec3u t\u1ea1i x = 0? B 2. C V\u00f4 s\u1ed1. D 1. A 3. \u0253 L\u1eddi gi\u1ea3i. Ta c\u00f3 y = 8x7 + 5(m \u2212 1)x4 \u2212 4(m2 \u2212 1)x3 + 1 = x3 [8x4 + 5(m \u2212 1)x \u2212 4(m2 \u2212 1)], \u00f1x = 0 y = 0 \u21d4 8x4 + 5(m \u2212 1)x \u2212 4(m2 \u2212 1) = 0 (\u2217) N\u1ebfu m = 1 th\u00ec y = 8x7, suy ra h\u00e0m s\u1ed1 \u0111\u1ea1t c\u1ef1c ti\u1ec3u t\u1ea1i x = 0. \u00f1x = 0 \uf8eex = 0 (nghi\u1ec7m k\u00e9p) N\u1ebfu m = \u22121 th\u00ec y = 0 \u21d4 8x4 \u2212 10x = 0 \u21d4 \uf8f0 \u2026 5 \u21d2 x = 0 kh\u00f4ng ph\u1ea3i l\u00e0 c\u1ef1c x = 3 tr\u1ecb. 4 N\u1ebfu m = \u00b11 th\u00ec x = 0 l\u00e0 nghi\u1ec7m \u0111\u01a1n. \u0110\u1eb7t g(x) = 8x4 + 5(m \u2212 1)x \u2212 4(m2 \u2212 1). H\u00e0m s\u1ed1 \u0111\u00e3 cho \u0111\u1ea1t c\u1ef1c ti\u1ec3u t\u1ea1i x = 0 khi ch\u1ec9 khi lim g(x) > 0 \u21d4 \u22124(m2 \u2212 1) > 0 \u21d4 m2 \u2212 1 < 0 \u21d4 \u22121 < m < 1. x\u21920\u2212 V\u00ec m \u2208 Z n\u00ean m = 0. V\u1eady gi\u00e1 tr\u1ecb m th\u1ecfa m\u00e3n y\u00eau c\u1ea7u b\u00e0i to\u00e1n l\u00e0 m = 0, m = 1. Ch\u1ecdn \u0111\u00e1p \u00e1n B \u0104 C\u00e2u 92 (C\u00e2u 47 - M\u0110 103 - BGD&\u0110T - N\u0103m 2017 - 2018). C\u00f3 bao nhi\u00eau gi\u00e1 tr\u1ecb nguy\u00ean c\u1ee7a tham s\u1ed1 m \u0111\u1ec3 h\u00e0m s\u1ed1 y = x8 + (m \u2212 4)x5 \u2212 (m2 \u2212 16)x4 + 1 \u0111\u1ea1t c\u1ef1c ti\u1ec3u t\u1ea1i x = 0. A 8. B V\u00f4 s\u1ed1. C 7. D 9. \u0253 L\u1eddi gi\u1ea3i. Ta c\u00f3 y = 8x7 + 5(m \u2212 4)x4 \u2212 4(m2 \u2212 16)x3. \u0110\u1eb7t g(x) = 8x4 + 5(m \u2212 4)x \u2212 4(m2 \u2212 16). C\u00f3 2 tr\u01b0\u1eddng h\u1ee3p c\u1ea7n x\u00e9t li\u00ean quan (m2 \u2212 16): Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t 68 S\u0110T: 0905.193.688","Ch\u01b0\u01a1ng 1. \u1ee8NG D\u1ee4NG \u0110\u1ea0O H\u00c0M \u0110\u1ec2 KH\u1ea2O S\u00c1T V\u00c0 V\u1ebc \u0110\u1ed2 TH\u1eca C\u1ee6A H\u00c0M S\u1ed0 Tr\u01b0\u1eddng h\u1ee3p 1: m2 \u2212 16 = 0 \u21d4 m = \u00b14. + Khi m = 4 ta c\u00f3 y = 8x7 \u21d2 x = 0 l\u00e0 \u0111i\u1ec3m c\u1ef1c ti\u1ec3u. + Khi m = \u22124 ta c\u00f3 y = x4(8x4 \u2212 40) \u21d2 x = 0 kh\u00f4ng l\u00e0 \u0111i\u1ec3m c\u1ef1c ti\u1ec3u. Tr\u01b0\u1eddng h\u1ee3p 2: m2 \u2212 16 = 0 \u21d4 m = \u00b14. Khi \u0111\u00f3 x = 0 kh\u00f4ng l\u00e0 nghi\u1ec7m c\u1ee7a g(x). Ta c\u00f3 x3 \u0111\u1ed5i d\u1ea5u t\u1eeb \u2212 sang + khi qua x0 = 0, do \u0111\u00f3 y = x3 \u00b7 g(x) \u0111\u1ed5i d\u1ea5u t\u1eeb \u2212 sang + khi qua x0 = 0 \u21d4 lim g(x) > 0 \u21d4 m2 \u2212 16 < 0. x\u21920 K\u1ebft h\u1ee3p c\u00e1c tr\u01b0\u1eddng h\u1ee3p gi\u1ea3i \u0111\u01b0\u1ee3c ta nh\u1eadn m \u2208 {\u22123; \u22122; \u22121; 0; 1; 2; 3; 4}. Ch\u1ecdn \u0111\u00e1p \u00e1n A \u0104 C\u00e2u 93 (C\u00e2u 42 - M\u0110 104 - BGD&\u0110T - N\u0103m 2017 - 2018). C\u00f3 bao nhi\u00eau gi\u00e1 tr\u1ecb nguy\u00ean c\u1ee7a tham s\u1ed1 m \u0111\u1ec3 h\u00e0m s\u1ed1 y = x8 + (m \u2212 3) x5 \u2212 (m2 \u2212 9) x4 + 1 \u0111\u1ea1t c\u1ef1c ti\u1ec3u t\u1ea1i x = 0 A 4. B 7. C 6. D V\u00f4 s\u1ed1. \u0253 L\u1eddi gi\u1ea3i. Ta c\u00f3 y = 8x7 + 5(m \u2212 3)x4 \u2212 4(m2 \u2212 9)x3. \u21d2y = 0 \u21d4 x3 8x4 + 5(m \u2212 3)x \u2212 4(m2 \u2212 9) \u00f1x = 0 = 0 \u21d4 g(x) = 8x4 + 5(m \u2212 3)x \u2212 4(m2 \u2212 9) = 0. X\u00e9t h\u00e0m s\u1ed1 g(x) = 8x4 + 5(m \u2212 3)x \u2212 4(m2 \u2212 9) c\u00f3 g (x) = 32x3 + 5(m \u2212 3). Ta th\u1ea5y g (x) = 0 c\u00f3 m\u1ed9t nghi\u1ec7m n\u00ean g(x) = 0 c\u00f3 t\u1ed1i \u0111a hai nghi\u1ec7m. N\u1ebfu g(x) = 0 c\u00f3 nghi\u1ec7m x = 0 \u21d2 m = 3 ho\u1eb7c m = \u22123. V\u1edbi m = 3 th\u00ec x = 0 l\u00e0 nghi\u1ec7m b\u1ed9i 4 c\u1ee7a g(x). Khi \u0111\u00f3 x = 0 l\u00e0 nghi\u1ec7m b\u1ed9i 7 c\u1ee7a y v\u00e0 y \u0111\u1ed5i d\u1ea5u t\u1eeb \u00e2m sang d\u01b0\u01a1ng khi \u0111i qua \u0111i\u1ec3m x = 0 n\u00ean x = 0 l\u00e0 \u0111i\u1ec3m c\u1ef1c ti\u1ec3u c\u1ee7a h\u00e0m s\u1ed1. V\u1eady m = 3 th\u1ecfa m\u00e3n. \uf8eex = 0 V\u1edbi m = \u22123 th\u00ec g(x) = 8x4 \u2212 30x = 0 \u21d4 \uf8f0 \u2026 15 x = 3 . 4 B\u1ea3ng x\u00e9t d\u1ea5u x \u2212\u221e 0 \u2026 15 +\u221e 3 4 y \u22120\u22120+ D\u1ef1a v\u00e0o b\u1ea3ng x\u00e9t d\u1ea5u ta th\u1ea5y x = 0 kh\u00f4ng l\u00e0 \u0111i\u1ec3m c\u1ef1c ti\u1ec3u do \u0111\u00f3 m = \u22123 kh\u00f4ng th\u1ecfa m\u00e3n. N\u1ebfu g(0) = 0 \u21d2 m = \u00b13. \u0110\u1ec3 h\u00e0m s\u1ed1 \u0111\u1ea1t c\u1ef1c ti\u1ec3u t\u1ea1i x = 0 \u21d2 g(0) > 0 \u21d4 m2 \u2212 9 < 0 \u21d4 \u22123 < m < 3. Do m \u2208 Z n\u00ean m \u2208 {\u22122; \u22121; 0; 1; 2}. V\u1eady c\u1ea3 hai tr\u01b0\u1eddng h\u1ee3p c\u00f3 6 gi\u00e1 tr\u1ecb nguy\u00ean m th\u1ecfa m\u00e3n. Ch\u1ecdn \u0111\u00e1p \u00e1n C \u0104 C\u00e2u 94 (C\u00e2u 46 - \u0110TK - BGD&\u0110T - N\u0103m 2016 - 2017). G\u1ecdi S l\u00e0 t\u1eadp h\u1ee3p t\u1ea5t c\u1ea3 c\u00e1c gi\u00e1 tr\u1ecb th\u1ef1c c\u1ee7a tham s\u1ed1 m \u0111\u1ec3 \u0111\u1ed3 th\u1ecb c\u1ee7a h\u00e0m s\u1ed1 y = 1 x3 \u2212 mx2 + 3 (m2 \u2212 1)x c\u00f3 hai \u0111i\u1ec3m c\u1ef1c tr\u1ecb l\u00e0 A v\u00e0 B sao cho A, B n\u1eb1m kh\u00e1c ph\u00eda v\u00e0 c\u00e1ch \u0111\u1ec1u \u0111\u01b0\u1eddng th\u1eb3ng d : y = 5x \u2212 9. T\u00ednh t\u1ed5ng t\u1ea5t c\u1ea3 c\u00e1c ph\u1ea7n t\u1eed c\u1ee7a S. Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t 69 S\u0110T: 0905.193.688","A 0. B 6. 2. C\u1ef1c tr\u1ecb c\u1ee7a h\u00e0m s\u1ed1 D 3. C \u22126. \u0253 L\u1eddi gi\u1ea3i. y = 1 x3 \u2212 mx2 + (m2 \u2212 1)x \u21d2 y = x2 \u2212 2mx + (m2 \u2212 1) 3 \u2206 = m2 \u2212 (m2 \u2212 1) = 1 \u00f1x = m + 1 \u00c5 m3 \u2212 3m \u2212 2 \u00e3 \u00c5 m3 \u2212 3m + 2 \u00e3 y =0\u21d4 x=m\u22121 \u21d2 A m + 1, 3 ; B m \u2212 1, 3 Hai \u0111i\u1ec3m A, B kh\u00e1c ph\u00eda v\u1edbi \u0111\u01b0\u1eddng th\u1eb3ng d v\u00e0 c\u00f3 kho\u1ea3ng c\u00e1ch t\u1edbi d b\u1eb1ng nhau t\u1ee9c l\u00e0 trung \u0111i\u1ec3m I c\u1ee7a AB thu\u1ed9c \u0111\u01b0\u1eddng th\u1eb3ng d, ta c\u00f3: I \u00c5 m3 \u2212 3m \u00e3 \u2208 (d) \u21d2 m3 \u2212 18m + 27 = 0 m, 3 \uf8eem = 3 \u221a Ta c\u00f3 (m \u2212 3)(m2 + 3m \u2212 9) = 0 \u21d4 \uf8f0 \u22123 \u00b1 3 5 m= 2 V\u1eady t\u1ed5ng c\u00e1c ph\u1ea7n t\u1eed c\u1ee7a S b\u1eb1ng 0. Ch\u1ecdn \u0111\u00e1p \u00e1n A \u0104 C\u00e2u 95 (C\u00e2u 43 - \u0110TK - BGD&\u0110T - N\u0103m 2017 - 2018). C\u00f3 bao nhi\u00eau gi\u00e1 tr\u1ecb nguy\u00ean c\u1ee7a tham s\u1ed1 m \u0111\u1ec3 h\u00e0m s\u1ed1 y = |3x4 \u2212 4x3 \u2212 12x2 + m| c\u00f3 7 \u0111i\u1ec3m c\u1ef1c tr\u1ecb A 3. B 5. C 6. D 4. \u0253 L\u1eddi gi\u1ea3i. X\u00e9t h\u00e0m s\u1ed1 f (x) = 3x4 \u2212 4x3 \u2212 12x2 ta c\u00f3 f (x) = 12x x2 \u2212 x \u2212 2 , f (x) = 0 \u21d4 x = \u22121, x = 0, x = 2. L\u1eadp b\u1ea3ng bi\u1ebfn thi\u00ean. x \u2212\u221e \u22121 0 2 +\u221e f (x) \u22120+0\u22120+ +\u221e 0 +\u221e f (x) \u22125 \u221232 Ta th\u1ea5y y\u00eau c\u1ea7u b\u00e0i to\u00e1n \u0111\u01b0\u1ee3c th\u1ecfa m\u00e3n khi v\u00e0 ch\u1ec9 khi \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 f (x) + m c\u1eaft tr\u1ee5c Ox t\u1ea1i 4 \u0111i\u1ec3m ph\u00e2n bi\u1ec7t, hay 0 < m < 5 n\u00ean ta c\u00f3 4 s\u1ed1 nguy\u00ean m. Ch\u1ecdn \u0111\u00e1p \u00e1n D \u0104 C\u00e2u 96 (C\u00e2u 44 - M\u0110 103 - BGD&\u0110T - \u0110\u1ee3t 1 - N\u0103m 2019 - 2020). Cho h\u00e0m s\u1ed1 b\u1eadc b\u1ed1n f (x) c\u00f3 b\u1ea3ng bi\u1ebfn thi\u00ean nh\u01b0 sau: Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t 70 S\u0110T: 0905.193.688","Ch\u01b0\u01a1ng 1. \u1ee8NG D\u1ee4NG \u0110\u1ea0O H\u00c0M \u0110\u1ec2 KH\u1ea2O S\u00c1T V\u00c0 V\u1ebc \u0110\u1ed2 TH\u1eca C\u1ee6A H\u00c0M S\u1ed0 x \u2212\u221e \u22121 0 1 +\u221e y \u22120+0\u22120+ +\u221e 3 +\u221e y \u22121 \u22121 S\u1ed1 \u0111i\u1ec3m c\u1ef1c tr\u1ecb c\u1ee7a h\u00e0m s\u1ed1 g(x) = x4[f (x \u2212 1)]2 l\u00e0 A 7. B 5. C 9. D 11. \u0253 L\u1eddi gi\u1ea3i. Ta c\u00f3 : f (x) = 4x4 \u2212 8x2 + 3 \u21d2 f (x) = 16x(x2 \u2212 1) Ta c\u00f3 g (x) = 2x3.f (x \u2212 1)2[.f (x \u2212 1) + x.f (x \u2212 1)] \uf8eex3 = 0 g (x) = 0 \u21d4 \uf8eff (x \u2212 1) = 0 \uf8f0 2f (x \u2212 1) + x.f (x \u2212 1) = 0 Ph\u01b0\u01a1ng tr\u00ecnh x3 = 0 c\u00f3 x = 0 (nghi\u1ec7m b\u1ed9i ba). Ph\u01b0\u01a1ng tr\u00ecnh f (x \u2212 1) = 0 c\u00f3 c\u00f9ng s\u1ed1 nghi\u1ec7m v\u1edbi ph\u01b0\u01a1ng tr\u00ecnh f (x) = 0 n\u00ean (2) c\u00f3 4 nghi\u1ec7m \u0111\u01a1n. Ph\u01b0\u01a1ng tr\u00ecnh 2f (x \u2212 1) + x \u00b7 f (x \u2212 1) = 0 c\u00f3 c\u00f9ng s\u1ed1 nghi\u1ec7m v\u1edbi ph\u01b0\u01a1ng tr\u00ecnh : 2f (x) + (x + 1) \u00b7 f (x) = 0 \u21d4 2(4x4 \u2212 8x2 + 3) + 16x(x + 1)(x2 \u2212 1) = 0 \u21d4 24x4 + 16x3 \u2212 32x2 \u2212 16x + 6 = 0 c\u00f3 4 nghi\u1ec7m ph\u00e2n bi\u1ec7t. D\u1ec5 th\u1ea5y 9 nghi\u1ec7m tr\u00ean ph\u00e2n bi\u1ec7t n\u00ean h\u00e0m s\u1ed1 g(x) = 0 c\u00f3 t\u1ea5t c\u1ea3 9 \u0111i\u1ec3m c\u1ef1c tr\u1ecb. Ch\u1ecdn \u0111\u00e1p \u00e1n C \u0104 C\u00e2u 97 (C\u00e2u 50 - M\u0110 101 - BGD&\u0110T - \u0110\u1ee3t 1 - N\u0103m 2020 - 2021). Cho h\u00e0m s\u1ed1 y = f (x) c\u00f3 \u0111\u1ea1o h\u00e0m f (x) = (x \u2212 7) (x2 \u2212 9), \u2200 x \u2208 R. C\u00f3 bao nhi\u00eau gi\u00e1 tr\u1ecb nguy\u00ean d\u01b0\u01a1ng c\u1ee7a tham s\u1ed1 m \u0111\u1ec3 h\u00e0m s\u1ed1 g(x) = f (|x3 + 5x| + m) c\u00f3 \u00edt nh\u1ea5t 3 \u0111i\u1ec3m c\u1ef1c tr\u1ecb? A 6. B 7. C 5. D 4. \u0253 L\u1eddi gi\u1ea3i. Ta c\u00f3 g (x) = (|x3 + 5x|) \u00b7f (|x3 + 5x| + m). Do \u00f1 x3 + 5x =0 =0 (1) \u0111\u00f3 g (x) = 0 \u21d4 x3 + 5x +m (2). f |x3 5x| \u00aex3 + 5x khi x \u2265 0 \u00ae3x2 + 5 khi x > 0 X\u00e9t h\u00e0m s\u1ed1 u(x) = + = \u2212 x3 \u2212 \u21d2 u (x) = khi x < 0. 5x khi x < 0 \u2212 3x2 \u2212 5 B\u1ea3ng bi\u1ebfn thi\u00ean c\u1ee7a h\u00e0m s\u1ed1 u(x) = |x3 + 5x| nh\u01b0 sau Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t 71 S\u0110T: 0905.193.688","2. C\u1ef1c tr\u1ecb c\u1ee7a h\u00e0m s\u1ed1 x \u2212\u221e 0 +\u221e +\u221e u (x) \u2212 + +\u221e u(x) 0 Suy ra u (x) \u0111\u1ed5i d\u1ea5u khi \u0111i qua x = 0. \uf8ee x3 + 5x = 7 \u2212 m \uf8ee x3 + 5x + m = 7 Ta c\u00f3 f (|x3 + 5x| + m) = 0 \u21d4 \uf8ef x3 + 5x + m = 3 \u21d4 \uf8ef x3 + 5x = 3 \u2212 m \uf8f0\uf8f0 x3 + 5x + m = \u22123 x3 + 5x = \u22123 \u2212 m. H\u00e0m s\u1ed1 g(x) c\u00f3 \u00edt nh\u1ea5t ba \u0111i\u1ec3m c\u1ef1c tr\u1ecb khi v\u00e0 ch\u1ec9 khi ph\u01b0\u01a1ng tr\u00ecnh g (x) = 0 c\u00f3 \u00edt nh\u1ea5t hai nghi\u1ec7m ph\u00e2n bi\u1ec7t kh\u00e1c 0 v\u00e0 g (x) \u0111\u1ed5i d\u1ea5u khi \u0111i qua \u00edt nh\u1ea5t hai trong s\u1ed1 c\u00e1c nghi\u1ec7m \u0111\u00f3. M\u1eb7t kh\u00e1c \u22123 \u2212 m < 3 \u2212 m < 7 \u2212 m. K\u1ebft h\u1ee3p v\u1edbi b\u1ea3ng bi\u1ebfn thi\u00ean h\u00e0m s\u1ed1 u(x) ta \u0111\u01b0\u1ee3c 7 \u2212 m > 0 \u21d4 m < 7 \u21d2 m \u2208 {1; 2; 3; 4; 5; 6}. V\u1eady c\u00f3 6 gi\u00e1 tr\u1ecb c\u1ee7a m th\u1ecfa m\u00e3n y\u00eau c\u1ea7u b\u00e0i to\u00e1n. C\u00e1ch 2. Ta th\u1ea5y x = 0 l\u00e0 tr\u1ee5c \u0111\u1ed1i x\u1ee9ng c\u1ee7a \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 y = g(x). Do \u0111\u00f3 YCBT \u21d4 H\u00e0m s\u1ed1 h(x) = f (x3 + 5x + m) c\u00f3 \u00edt nh\u1ea5t m\u1ed9t \u0111i\u1ec3m c\u1ef1c tr\u1ecb x \u2208 (0; +\u221e). Ta c\u00f3 h (x) = (3x2 + 5) \u00b7 f (x3 + 5x + m), \uf8eex3 + 5x + m = 7 \uf8ee \u2212 x3 \u2212 5x + 7 = m h (x) = 0 \u21d4 \uf8efx3 + 5x + m = 3 \u21d4 \uf8ef \u2212 x3 \u2212 5x + 3 = m \uf8f0\uf8f0 x3 + 5x + m = \u22123 \u2212 x3 \u2212 5x \u2212 3 = m. y 7 y=m 3 Ox \u22123 T\u1eeb \u0111\u00f3 ta \u0111\u01b0\u1ee3c m < 7 \u21d2 m \u2208 {1; 2; 3; 4; 5; 6}. V\u1eady c\u00f3 6 gi\u00e1 tr\u1ecb c\u1ee7a m th\u1ecfa m\u00e3n y\u00eau c\u1ea7u b\u00e0i to\u00e1n. Ch\u1ecdn \u0111\u00e1p \u00e1n A \u0104 C\u00e2u 98 (C\u00e2u 49 - M\u0110 102 - BGD&\u0110T - \u0110\u1ee3t 1 - N\u0103m 2020 - 2021). Cho h\u00e0m s\u1ed1 y = f (x) c\u00f3 \u0111\u1ea1o h\u00e0m f (x) = (x \u2212 8)(x2 \u2212 9), \u2200x \u2208 R. C\u00f3 bao nhi\u00eau gi\u00e1 tr\u1ecb nguy\u00ean d\u01b0\u01a1ng c\u1ee7a tham s\u1ed1 m \u0111\u1ec3 h\u00e0m s\u1ed1 g(x) = f (|x3 + 6x| + m) c\u00f3 \u00edt nh\u1ea5t 3 \u0111i\u1ec3m c\u1ef1c tr\u1ecb? A 5. B 7. C 8. D 6. \u0253 L\u1eddi gi\u1ea3i. Ta th\u1ea5y h\u00e0m g(x) = f (|x3 + 6x| + m) = f ((x2 + 6) |x| + m) l\u00e0 h\u00e0m s\u1ed1 ch\u1eb5n n\u00ean \u0111\u1ed3 th\u1ecb nh\u1eadn tr\u1ee5c tung l\u00e0m tr\u1ee5c \u0111\u1ed1i x\u1ee9ng. Do \u0111\u00f3 \u0111\u1ec3 h\u00e0m g(x) = f (|x3 + 6x| + m) c\u00f3 \u00edt nh\u1ea5t 3 \u0111i\u1ec3m c\u1ef1c tr\u1ecb th\u00ec h\u00e0m s\u1ed1 Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t 72 S\u0110T: 0905.193.688","Ch\u01b0\u01a1ng 1. \u1ee8NG D\u1ee4NG \u0110\u1ea0O H\u00c0M \u0110\u1ec2 KH\u1ea2O S\u00c1T V\u00c0 V\u1ebc \u0110\u1ed2 TH\u1eca C\u1ee6A H\u00c0M S\u1ed0 h(x) = f (x3 + 6x + m) c\u00f3 \u00edt nh\u1ea5t 1 \u0111i\u1ec3m c\u1ef1c tr\u1ecb c\u00f3 ho\u00e0nh \u0111\u1ed9 d\u01b0\u01a1ng, t\u1ee9c l\u00e0 ph\u01b0\u01a1ng tr\u00ecnh h (x) = (3x2 + 6)f (x3 + 6x + m) = 0 c\u00f3 nghi\u1ec7m d\u01b0\u01a1ng b\u1ed9i l\u1ebb \uf8eex3 + 3x + m = 8 \uf8eex3 + 3x = 8 \u2212 m \u21d4 \uf8efx3 + 3x + m = 3 \u21d4 \uf8efx3 + 3x = 3 \u2212 m c\u00f3 nghi\u1ec7m d\u01b0\u01a1ng b\u1ed9i l\u1ebb. \uf8f0\uf8f0 x3 + 3x + m = \u22123 x3 + 3x = \u22123 \u2212 m X\u00e9t h\u00e0m s\u1ed1 k(x) = x3 + 3x, v\u1edbi x > 0. x0 +\u221e k (x) = 3x2 + 3 > 0, \u2200x > 0. k (x) + Ta c\u00f3 b\u1ea3ng bi\u1ebfn thi\u00ean c\u1ee7a k(x) nh\u01b0 h\u00ecnh b\u00ean. T\u1eeb b\u1ea3ng bi\u1ebfn thi\u00ean, suy ra ph\u01b0\u01a1ng tr\u00ecnh h (x) = 0 c\u00f3 nghi\u1ec7m d\u01b0\u01a1ng k(x) +\u221e b\u1ed9i l\u1ebb khi v\u00e0 ch\u1ec9 khi 8 \u2212 m > 0 \u21d4 m < 8. 0 V\u00ec m nguy\u00ean d\u01b0\u01a1ng n\u00ean m \u2208 {1; 2; 3; 4; 5; 6; 7}. V\u1eady c\u00f3 7 gi\u00e1 tr\u1ecb c\u1ee7a m th\u1ecfa m\u00e3n y\u00eau c\u1ea7u b\u00e0i to\u00e1n. Ch\u1ecdn \u0111\u00e1p \u00e1n B \u0104 C\u00e2u 99 (C\u00e2u 50 - M\u0110 103 - BGD&\u0110T - \u0110\u1ee3t 1 - N\u0103m 2020 - 2021). Cho h\u00e0m s\u1ed1 y = f (x) c\u00f3 \u0111\u1ea1o h\u00e0m f (x) = (x \u2212 10)(x2 \u2212 25), \u2200x \u2208 R. C\u00f3 bao nhi\u00eau gi\u00e1 tr\u1ecb nguy\u00ean d\u01b0\u01a1ng c\u1ee7a tham s\u1ed1 m \u0111\u1ec3 h\u00e0m s\u1ed1 g(x) = f (|x3 + 8x| + m) c\u00f3 \u00edt nh\u1ea5t 3 \u0111i\u1ec3m c\u1ef1c tr\u1ecb? A 9. B 25. C 5. D 10. \u0253 L\u1eddi gi\u1ea3i. X\u00e9t h\u00e0m s\u1ed1 g(x) = f (|x3 + 8x| + m). H\u00e0m s\u1ed1 g(x) l\u00e0 h\u00e0m s\u1ed1 ch\u1eb5n n\u00ean \u0111\u1ed3 th\u1ecb nh\u1eadn tr\u1ee5c Oy l\u00e0m tr\u1ee5c \u0111\u1ed1i x\u1ee9ng. Do \u0111\u00f3 ta nh\u1eadn th\u1ea5y x = 0 l\u00e0 m\u1ed9t \u0111i\u1ec3m c\u1ef1c tr\u1ecb c\u1ee7a h\u00e0m s\u1ed1 g(x). V\u1edbi x = 0 ta c\u00f3 g (x) = x3 + 8x + m f x3 + 8x + m = (3x2 + 8)(x3 + 8x) f x3 + 8x + m . |x3 + 8x| Ta c\u00f3 \uf8ee x3 + 8x + m = 10 \uf8ee x3 + 8x = 10 \u2212 m f x3 + 8x + m = 0 \u21d4 \uf8ef x3 + 8x + m = 5 \u21d4 \uf8ef x3 + 8x = 5 \u2212 m \uf8f0\uf8f0 x3 + 8x + m = \u22125 x3 + 8x = \u22125 \u2212 m. X\u00e9t h\u00e0m s\u1ed1 h(x) = x3 + 8x. V\u00ec h (x) = 3x2 + 8 > 0, \u2200x \u2208 R n\u00ean h(x) \u0111\u1ed3ng bi\u1ebfn tr\u00ean R. Ta c\u00f3 b\u1ea3ng bi\u1ebfn thi\u00ean c\u1ee7a h\u00e0m s\u1ed1 k(x) = |h(x)| = |x3 + 8x| nh\u01b0 sau x \u2212\u221e 0 +\u221e +\u221e +\u221e k(x) 0 \u0110\u1ec3 h\u00e0m s\u1ed1 g(x) = f (|x3 + 8x| + m) c\u00f3 \u00edt nh\u1ea5t 3 \u0111i\u1ec3m c\u1ef1c tr\u1ecb th\u00ec ph\u01b0\u01a1ng tr\u00ecnh g (x) = 0 c\u00f3 \u00edt nh\u1ea5t 2 nghi\u1ec7m ph\u00e2n bi\u1ec7t kh\u00e1c 0 v\u00e0 g (x) \u0111\u1ed5i d\u1ea5u khi x \u0111i qua \u00edt nh\u1ea5t 2 trong c\u00e1c nghi\u1ec7m \u0111\u00f3. T\u1eeb b\u1ea3ng bi\u1ebfn thi\u00ean c\u1ee7a h\u00e0m s\u1ed1 k(x) ta th\u1ea5y \u0111i\u1ec1u n\u00e0y ch\u1ec9 x\u1ea3y ra khi v\u00e0 ch\u1ec9 khi 10 \u2212 m > 0 \u21d4 m < 10. Do m nguy\u00ean d\u01b0\u01a1ng n\u00ean c\u00f3 9 gi\u00e1 tr\u1ecb nguy\u00ean d\u01b0\u01a1ng c\u1ee7a m th\u1ecfa m\u00e3n \u0111\u1ec1 b\u00e0i l\u00e0 {1; 2; 3; 4; 5; 6; 7; 8; 9} . Ch\u1ecdn \u0111\u00e1p \u00e1n A Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t 73 S\u0110T: 0905.193.688","2. C\u1ef1c tr\u1ecb c\u1ee7a h\u00e0m s\u1ed1 \u0104 C\u00e2u 100 (C\u00e2u 49 - M\u0110 102 - BGD&\u0110T - \u0110\u1ee3t 2 - N\u0103m 2020 - 2021). Cho h\u00e0m s\u1ed1 f (x) = x4 \u2212 12x3 + 30x2 + (3 \u2212 m)x, v\u1edbi m l\u00e0 tham s\u1ed1 th\u1ef1c. C\u00f3 bao nhi\u00eau gi\u00e1 tr\u1ecb nguy\u00ean c\u1ee7a m \u0111\u1ec3 h\u00e0m s\u1ed1 g(x) = f (|x|) c\u00f3 \u0111\u00fang 7 \u0111i\u1ec3m c\u1ef1c tr\u1ecb? A 25. B 27. C 26. D 28. \u0253 L\u1eddi gi\u1ea3i. H\u00e0m s\u1ed1 f (x) x\u00e1c \u0111\u1ecbnh tr\u00ean R v\u00e0 c\u00f3 \u0111\u1ea1o h\u00e0m f (x) = 4x3 \u2212 36x2 + 60x + 3 \u2212 m. Ta th\u1ea5y f (x) = 0 \u21d4 4x3 \u2212 36x2 + 60x + 3 = m. (1) H\u00e0m s\u1ed1 g(x) = f (|x|) c\u00f3 \u0111\u00fang 7 \u0111i\u1ec3m c\u1ef1c tr\u1ecb khi v\u00e0 ch\u1ec9 khi f (x) = 0 c\u00f3 ba nghi\u1ec7m ph\u00e2n bi\u1ec7t d\u01b0\u01a1ng. \u0110\u1eb7t h(x) = 4x3 \u2212 36x2 + 60x + 3, ta c\u00f3 h (x) = 12x2 \u2212 72x + 60; h (x) = 0 \u21d4 \u00f1x = 1 x = 5. B\u1ea3ng bi\u1ebfn thi\u00ean c\u1ee7a h\u00e0m s\u1ed1 h(x) MDD-109 x \u2212\u221e 0 1 5 +\u221e h (x) + | +0\u22120+ 31 +\u221e h(x) 3 \u2212\u221e \u221297 Ph\u01b0\u01a1ng tr\u00ecnh (1) l\u00e0 ph\u01b0\u01a1ng tr\u00ecnh ho\u00e0nh \u0111\u1ed9 giao \u0111i\u1ec3m c\u1ee7a \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 y = h(x) v\u00e0 \u0111\u01b0\u1eddng th\u1eb3ng y = m. D\u1ef1a v\u00e0o b\u1ea3ng bi\u1ebfn thi\u00ean ta th\u1ea5y ph\u01b0\u01a1ng tr\u00ecnh (1) c\u00f3 ba nghi\u1ec7m ph\u00e2n bi\u1ec7t d\u01b0\u01a1ng khi v\u00e0 ch\u1ec9 khi m \u2208 (3; 31). K\u1ebft h\u1ee3p gi\u1ea3 thi\u1ebft m nguy\u00ean ta \u0111\u01b0\u1ee3c m \u2208 {4; 5; 6; . . . ; 30}. V\u1eady c\u00f3 27 gi\u00e1 tr\u1ecb m th\u1ecfa m\u00e3n. Ch\u1ecdn \u0111\u00e1p \u00e1n B \u0104 C\u00e2u 101 (C\u00e2u 49 - M\u0110 103 - BGD&\u0110T - \u0110\u1ee3t 2 - N\u0103m 2020 - 2021). Cho h\u00e0m s\u1ed1 f (x) = x4 \u2212 10x3 + 24x2 + (4 \u2212 m)x v\u1edbi m l\u00e0 tham s\u1ed1 th\u1ef1c. C\u00f3 bao nhi\u00eau gi\u00e1 tr\u1ecb nguy\u00ean c\u1ee7a m \u0111\u1ec3 h\u00e0m s\u1ed1 g(x) = f (|x|) c\u00f3 \u0111\u00fang 7 \u0111i\u1ec3m c\u1ef1c tr\u1ecb? A 25. B 22. C 26. D 21. \u0253 L\u1eddi gi\u1ea3i. Ta c\u00f3 f (x) = 4x3 \u2212 30x2 + 48x + 4 \u2212 m. f (x) = 0 \u21d4 4x3 \u2212 30x2 + 48x + 4 \u2212 m = 0 \u21d4 m = 4x3 \u2212 30x2 + 48x + 4. (1) \u0110\u1ec3 h\u00e0m s\u1ed1 g(x) = f (|x|) c\u00f3 \u0111\u00fang 7 \u0111i\u1ec3m c\u1ef1c tr\u1ecb th\u00ec h\u00e0m s\u1ed1 f (x) ph\u1ea3i c\u00f3 3 \u0111i\u1ec3m c\u1ef1c tr\u1ecb d\u01b0\u01a1ng. Khi \u0111\u00f3 ph\u01b0\u01a1ng tr\u00ecnh f (x) = 0 ph\u1ea3i c\u00f3 3 nghi\u1ec7m d\u01b0\u01a1ng ph\u00e2n bi\u1ec7t t\u01b0\u01a1ng \u0111\u01b0\u01a1ng ph\u01b0\u01a1ng tr\u00ecnh (1) c\u00f3 3 nghi\u1ec7m d\u01b0\u01a1ng ph\u00e2n bi\u1ec7t. X\u00e9t h\u00e0m s\u1ed1 h(x) = 4x3 \u2212 30x2 + 48x + 4 tr\u00ean kho\u1ea3ng (0; +\u221e). Ta c\u00f3 h (x) = 12x2 \u2212 60x + 48. X\u00e9t h (x) = 0 \u21d4 \u00f1x = 1 x = 4. B\u1ea3ng bi\u1ebfn thi\u00ean c\u1ee7a h\u00e0m s\u1ed1 h(x) x 0 1 4 +\u221e y +0\u22120+ 26 +\u221e y 4 \u221228 Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t 74 S\u0110T: 0905.193.688","Ch\u01b0\u01a1ng 1. \u1ee8NG D\u1ee4NG \u0110\u1ea0O H\u00c0M \u0110\u1ec2 KH\u1ea2O S\u00c1T V\u00c0 V\u1ebc \u0110\u1ed2 TH\u1eca C\u1ee6A H\u00c0M S\u1ed0 \u0110\u1ec3 ph\u01b0\u01a1ng tr\u00ecnh m = 4x3 \u2212 30x2 + 48x + 4 c\u00f3 3 nghi\u1ec7m d\u01b0\u01a1ng ph\u00e2n bi\u1ec7t th\u00ec \u0111\u01b0\u1eddng th\u1eb3ng y = m c\u1eaft \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 y = h(x) t\u1ea1i 3 \u0111i\u1ec3m ph\u00e2n bi\u1ec7t c\u00f3 ho\u00e0nh \u0111\u1ed9 d\u01b0\u01a1ng. D\u1ef1a v\u00e0o b\u1ea3ng bi\u1ebfn thi\u00ean, ta suy ra 4 < m < 26. M\u00e0 m \u2208 Z n\u00ean m \u2208 {5; 6; . . . ; 25}. V\u1eady c\u00f3 21 gi\u00e1 tr\u1ecb nguy\u00ean m th\u1ecfa m\u00e3n y\u00eau c\u1ea7u b\u00e0i to\u00e1n. Ch\u1ecdn \u0111\u00e1p \u00e1n D \u0104 C\u00e2u 102 (C\u00e2u 50 - M\u0110 101 - BGD&\u0110T - N\u0103m 2021 - 2022). C\u00f3 bao nhi\u00eau gi\u00e1 tr\u1ecb nguy\u00ean d\u01b0\u01a1ng c\u1ee7a tham s\u1ed1 m \u0111\u1ec3 h\u00e0m s\u1ed1 y = |x4 \u2212 2mx2 + 64x| c\u00f3 \u0111\u00fang ba \u0111i\u1ec3m c\u1ef1c tr\u1ecb? A 5. B 6. C 12. D 11. \u0253 L\u1eddi gi\u1ea3i. X\u00e9t h\u00e0m s\u1ed1 g(x) = x4 \u2212 2mx2 + 64x; lim g(x) = +\u221e. x\u2192\u00b1\u221e \u00f1x = 0 g(x) = 0 \u21d4 x3 \u2212 2mx + 64 = 0. Suy ra ph\u01b0\u01a1ng tr\u00ecnh g(x) = 0 c\u00f3 \u00edt nh\u1ea5t hai nghi\u1ec7m \u0111\u01a1n ph\u00e2n bi\u1ec7t. Do \u0111\u00f3 h\u00e0m s\u1ed1 y = |g(x)| c\u00f3 \u0111\u00fang ba \u0111i\u1ec3m c\u1ef1c tr\u1ecb khi v\u00e0 ch\u1ec9 khi h\u00e0m s\u1ed1 y = g(x) c\u00f3 \u0111\u00fang m\u1ed9t \u0111i\u1ec3m c\u1ef1c tr\u1ecb. Ta c\u00f3 g (x) = 4x3 \u2212 4mx + 64. Do \u0111\u00f3 g (x) = 0 \u21d4 m = x2 + 16 (v\u00ec x = 0 kh\u00f4ng l\u00e0 nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh g (x) = 0). x 16 X\u00e9t h\u00e0m s\u1ed1 h(x) = x2 + x . Ta c\u00f3 h (x) = 2x \u2212 16 = .2x3\u221216 x2 x2 Do \u0111\u00f3 h (x) = 0 \u21d4 x = 2. Ta c\u00f3 b\u1ea3ng bi\u1ebfn thi\u00ean: x \u2212\u221e 0 2 +\u221e f (x) \u2212 \u22120+ +\u221e +\u221e +\u221e f (x) \u2212\u221e 12 T\u1eeb b\u1ea3ng bi\u1ebfn thi\u00ean suy ra m \u2264 12. V\u1eady c\u00f3 12 gi\u00e1 tr\u1ecb nguy\u00ean d\u01b0\u01a1ng c\u1ee7a m th\u1ecfa y\u00eau c\u1ea7u b\u00e0i to\u00e1n. Ch\u1ecdn \u0111\u00e1p \u00e1n C \u0104 C\u00e2u 103 (C\u00e2u 49 - M\u0110 104 - BGD&\u0110T - N\u0103m 2021 - 2022). C\u00f3 bao nhi\u00eau s\u1ed1 nguy\u00ean d\u01b0\u01a1ng c\u1ee7a tham s\u1ed1 m \u0111\u1ec3 h\u00e0m s\u1ed1 y = |x4 \u2212 mx2 \u2212 64x| c\u00f3 \u0111\u00fang 3 \u0111i\u1ec3m c\u1ef1c tr\u1ecb? A 23. B 12. C 24. D 11. \u0253 L\u1eddi gi\u1ea3i. X\u00e9t h\u00e0m s\u1ed1 g(x) = x4 \u2212 mx2 \u2212 64x; g (x) = 4x3 \u2212 2mx \u2212 64; c\u00f3 lim f (x) = +\u221e. x\u2192\u00b1\u221e \u00ef x=0 x3 \u2212 mx g(x) = 0 \u21d4 \u2212 64 = 0 \u21d2 g(x) = 0 c\u00f3 \u00edt nh\u1ea5t 2 nghi\u1ec7m ph\u00e2n bi\u1ec7t. Do \u0111\u00f3 h\u00e0m s\u1ed1 y = |g(x)| c\u00f3 \u0111\u00fang 3 \u0111i\u1ec3m c\u1ef1c tr\u1ecb \u21d4 h\u00e0m s\u1ed1 y = g(x) c\u00f3 \u0111\u00fang 1 c\u1ef1c tr\u1ecb \u21d4 g (x) \u0111\u1ed5i d\u1ea5u \u0111\u00fang 1 l\u1ea7n (*). Nh\u1eadn x\u00e9t n\u1ebfu x = 0 \u21d2 g (0) = \u221264 < 0 \u21d2 g(x) kh\u00f4ng c\u00f3 c\u1ef1c tr\u1ecb (hay x = 0 kh\u00f4ng th\u1ecfa m\u00e3n). Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t 75 S\u0110T: 0905.193.688","2. C\u1ef1c tr\u1ecb c\u1ee7a h\u00e0m s\u1ed1 N\u00ean g (x) = 0 \u21d4 m = 2x2 \u2212 32 \u00b7 \u0110\u1eb7t h(x) = 2x2 \u2212 32 \u00b7 xx x3 + 8 32 4 ; h (x) = 0 \u21d4 x = \u22122. C\u00f3 h (x) = 4x + = x2 x2 B\u1ea3ng bi\u1ebfn thi\u00ean x \u2212\u221e \u22122 0 +\u221e +\u221e h (x) \u22120+ + +\u221e +\u221e h(x) 24 \u2212\u221e T\u1eeb b\u1ea3ng bi\u1ebfn thi\u00ean suy ra (\u2217) \u21d4 m \u2264 24. K\u1ebft h\u1ee3p v\u1edbi \u0111i\u1ec1u ki\u1ec7n m nguy\u00ean d\u01b0\u01a1ng suy ra m \u2208 {1; 2; 3; ...; 24}. Ch\u1ecdn \u0111\u00e1p \u00e1n C Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t 76 S\u0110T: 0905.193.688","Ch\u01b0\u01a1ng 1. \u1ee8NG D\u1ee4NG \u0110\u1ea0O H\u00c0M \u0110\u1ec2 KH\u1ea2O S\u00c1T V\u00c0 V\u1ebc \u0110\u1ed2 TH\u1eca C\u1ee6A H\u00c0M S\u1ed0 B\u00c0I 3. GI\u00c1 TR\u1eca L\u1edaN NH\u1ea4T V\u00c0 GI\u00c1 TR\u1eca NH\u1ece NH\u1ea4T C\u1ee6A H\u00c0M S\u1ed0 \u0104 C\u00e2u 1 (C\u00e2u 8 - \u0110MH - BGD&\u0110T - N\u0103m 2018 - 2019). Cho h\u00e0m s\u1ed1 y = f (x) li\u00ean t\u1ee5c t\u00ean \u0111o\u1ea1n [\u22121; 3] c\u00f3 \u0111\u1ed3 th\u1ecb nh\u01b0 h\u00ecnh y 3 v\u1ebd b\u00ean. G\u1ecdi M v\u00e0 m l\u1ea7n l\u01b0\u1ee3t l\u00e0 gi\u00e1 tr\u1ecb l\u1edbn nh\u1ea5t, gi\u00e1 tr\u1ecb nh\u1ecf nh\u1ea5t 2 c\u1ee7a h\u00e0m s\u1ed1 \u0111\u00e3 cho tr\u00ean \u0111o\u1ea1n [\u22121; 3]. Gi\u00e1 tr\u1ecb c\u1ee7a M \u2212 m b\u1eb1ng 1 A 0. B 1. C 4. D 5. \u22121 O 2 3x \u22122 \u0253 L\u1eddi gi\u1ea3i. D\u1ef1a v\u00e0o \u0111\u1ed3 th\u1ecb ta c\u00f3 M = 3, m = \u22122. Do \u0111\u00f3 M \u2212 m = 5. Ch\u1ecdn \u0111\u00e1p \u00e1n D \u0104 C\u00e2u 2 (C\u00e2u 19 - M\u0110 103 - BGD&\u0110T - N\u0103m 2018 - 2019). Gi\u00e1 tr\u1ecb l\u1edbn nh\u1ea5t c\u1ee7a h\u00e0m s\u1ed1 f (x) = x3 \u2212 3x tr\u00ean \u0111o\u1ea1n [\u22123; 3] b\u1eb1ng A 18. B 2. C \u221218. D \u22122. \u0253 L\u1eddi gi\u1ea3i. Ta c\u00f3 y = 3x2 \u2212 3 = 0 \u21d4 x = \u00b11 \u2208 (\u22123; 3) f (\u22123) = \u221218; f (\u22121) = 2; f (1) = \u22122; f (3) = 18. V\u1eady gi\u00e1 tr\u1ecb l\u1edbn nh\u1ea5t c\u1ee7a h\u00e0m s\u1ed1 \u0111\u00e3 cho tr\u00ean [\u22123; 3] l\u00e0 18. Ch\u1ecdn \u0111\u00e1p \u00e1n A \u0104 C\u00e2u 3 (C\u00e2u 21 - M\u0110 104 - BGD&\u0110T - N\u0103m 2018 - 2019). Gi\u00e1 tr\u1ecb nh\u1ecf nh\u1ea5t c\u1ee7a h\u00e0m s\u1ed1 f (x) = x3 \u2212 3x tr\u00ean \u0111o\u1ea1n [\u22123; 3] b\u1eb1ng A 18. B \u221218. C \u22122. D 2. \u0253 L\u1eddi gi\u1ea3i. Ta c\u00f3 f (x) = 3x2 \u2212 3 = 0 \u21d4 \u00f1x = 1 \u2208 [\u22123; 3] x = \u22121 \u2208 [\u22123; 3]. Ta l\u1ea1i c\u00f3 f (\u22123) = \u221218; f (\u22121) = 2; f (1) = \u22122; f (3) = 18. V\u1eady gi\u00e1 tr\u1ecb nh\u1ecf nh\u1ea5t c\u1ee7a h\u00e0m s\u1ed1 f (x) tr\u00ean \u0111o\u1ea1n [\u22123; 3] b\u1eb1ng \u221218. Ch\u1ecdn \u0111\u00e1p \u00e1n B \u0104 C\u00e2u 4 (C\u00e2u 28 - \u0110TK - BGD&\u0110T - l\u1ea7n 2 - N\u0103m 2019 - 2020). Gi\u00e1 tr\u1ecb nh\u1ecf nh\u1ea5t c\u1ee7a h\u00e0m s\u1ed1 f (x) = x4 \u2212 10x2 + 2 tr\u00ean \u0111o\u1ea1n [\u22121; 2] b\u1eb1ng A 2. B \u221223. C \u221222. D \u22127. Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t \u0253 L\u1eddi gi\u1ea3i. S\u0110T: 0905.193.688 77","3. Gi\u00e1 tr\u1ecb l\u1edbn nh\u1ea5t v\u00e0 gi\u00e1 tr\u1ecb nh\u1ecf nh\u1ea5t c\u1ee7a h\u00e0m s\u1ed1 \uf8eex = 0 \u2208 [\u22121; 2] \u221a Ta c\u00f3 f (x) = 4x3 \u2212 20x; f (x) = 0 \u21d4 \uf8efx = \u2212 5 \u2208\/ [\u22121; 2] \uf8f0\u221a x = 5 \u2208\/ [\u22121; 2]. X\u00e9t f (\u22121) = \u22127, f (0) = 2, f (2) = \u221222. V\u1eady min f (x) = \u221222. [\u22121;2] Ch\u1ecdn \u0111\u00e1p \u00e1n C \u0104 C\u00e2u 5 (C\u00e2u 26 - M\u0110 102 - BGD&\u0110T - \u0110\u1ee3t 1 - N\u0103m 2019 - 2020). Gi\u00e1 tr\u1ecb nh\u1ecf nh\u1ea5t c\u1ee7a h\u00e0m s\u1ed1 f (x) \u221a= x3 \u2212 21x tr\u00ean \u0111o\u1ea1n\u221a[2; 19] b\u1eb1ng A \u221236. B \u221214 7. C 14 7. D \u221234. \u0253 L\u1eddi gi\u1ea3i. X\u00e9t tr\u00ean \u0111o\u1ea1n [2; 19] h\u00e0m s\u1ed1 li\u00ean t\u1ee5c. \u221a Ta c\u00f3 f (x) = 3x2 \u2212 21 . Cho f (x) = 0 \u21d2 3x2 \u2212 21 = 0 \u21d4 \u00f1 x = 7 \u2208 [2; 19] \u221a x = \u2212 7 \u2208\/ [2; 19] . \u00c4\u221a \u00e4 \u221a Khi \u0111\u00f3 f (2) = \u221234 , f 7 = \u221214 7 , f (19) = 6460. \u00c4\u221a \u00e4 \u221a V\u1eady min f (x) = f 7 = \u221214 7 . [2;19] Ch\u1ecdn \u0111\u00e1p \u00e1n B \u0104 C\u00e2u 6 (C\u00e2u 36 - M\u0110 103 - BGD&\u0110T - \u0110\u1ee3t 1 - N\u0103m 2020 - 2021). Tr\u00ean \u0111o\u1ea1n [0; 3], h\u00e0m s\u1ed1 y = x3 \u2212 3x + 4 \u0111\u1ea1t gi\u00e1 tr\u1ecb nh\u1ecf nh\u1ea5t t\u1ea1i \u0111i\u1ec3m A x = 1. B x = 0. C x = 3. D x = 2. \u0253 L\u1eddi gi\u1ea3i. Tr\u00ean [0; 3], h\u00e0m s\u1ed1 y = x3 \u2212 3x + 4 li\u00ean t\u1ee5c, c\u00f3 \u0111\u1ea1o h\u00e0m y = 3x2 \u2212 3 v\u00e0 y = 0 \u21d4 3x2 \u2212 3 = 0 \u21d4 x2 \u2212 1 = 0 \u21d4 \u00f1x = 1 x = \u22121 lo\u1ea1i v\u00ec \u2208\/ [0; 3]. Ta c\u00f3 y(0) = 4, y(1) = 2, y(3) = 22. V\u1eady h\u00e0m s\u1ed1 \u0111\u1ea1t gi\u00e1 tr\u1ecb nh\u1ecf nh\u1ea5t l\u00e0 2 t\u1ea1i x = 1. Ch\u1ecdn \u0111\u00e1p \u00e1n A \u0104 C\u00e2u 7 (C\u00e2u 35 - M\u0110 101 - BGD&\u0110T - \u0110\u1ee3t 2 - N\u0103m 2020 - 2021). Tr\u00ean \u0111o\u1ea1n [\u22124; \u22121] h\u00e0m s\u1ed1 y = x4 \u2212 8x2 + 13 \u0111\u1ea1t gi\u00e1 tr\u1ecb nh\u1ecf nh\u1ea5t t\u1ea1i \u0111i\u1ec3m A x = \u22122. B x = \u22121. C x = \u22124. D x = \u22123. \u0253 L\u1eddi gi\u1ea3i. H\u00e0m s\u1ed1 \u0111\u00e3 cho x\u00e1c \u0111\u1ecbnh v\u00e0 li\u00ean t\u1ee5c tr\u00ean \u0111o\u1ea1n [\u22124; \u22121]. Ta c\u00f3 y = 4x3 \u2212 16x. \uf8eex = 0 \u2208\/ [\u22124; \u22121] Ph\u01b0\u01a1ng tr\u00ecnh y = 0 \u21d4 \uf8efx = 2 \u2208\/ [\u22124; \u22121] \uf8f0 x = \u22122 \u2208 [\u22124; \u22121]. M\u1eb7t kh\u00e1c y(\u22124) = 141, y(\u22122) = \u22123, y(\u22121) = 6. V\u1eady h\u00e0m s\u1ed1 y = x4 \u2212 8x2 + 13 \u0111\u1ea1t gi\u00e1 tr\u1ecb nh\u1ecf nh\u1ea5t t\u1ea1i \u0111i\u1ec3m x = \u22122. Ch\u1ecdn \u0111\u00e1p \u00e1n A Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t 78 S\u0110T: 0905.193.688","Ch\u01b0\u01a1ng 1. \u1ee8NG D\u1ee4NG \u0110\u1ea0O H\u00c0M \u0110\u1ec2 KH\u1ea2O S\u00c1T V\u00c0 V\u1ebc \u0110\u1ed2 TH\u1eca C\u1ee6A H\u00c0M S\u1ed0 \u0104 C\u00e2u 8 (C\u00e2u 6 - \u0110MH - BGD&\u0110T - N\u0103m 2016 - 2017). x2 + 3 T\u00ecm gi\u00e1 tr\u1ecb nh\u1ecf nh\u1ea5t c\u1ee7a h\u00e0m s\u1ed1 y = tr\u00ean \u0111o\u1ea1n [2; 4]. x\u22121 19 A min y = 6. B min y = \u22122. C min y = \u22123. D min y = . [2;4] 3 [2;4] [2;4] [2;4] \u0253 L\u1eddi gi\u1ea3i. Ta c\u00f3 y = x2 \u2212 2x \u2212 3 = 0 \u21d2 \u00f1x = \u22121 (lo\u1ea1i) (x \u2212 1)2 x=3 (Do x\u00e9t tr\u00ean \u0111o\u1ea1n [2; 4]). 19 y(3) = 6; y(2) = 7; y(4) = , suy ra min y = 6. 3 [2;4] Ch\u1ecdn \u0111\u00e1p \u00e1n A \u0104 C\u00e2u 9 (C\u00e2u 7 - \u0110TN - BGD&\u0110T - N\u0103m 2016 - 2017). M\u1ed9t v\u1eadt chuy\u1ec3n \u0111\u1ed9ng theo quy lu\u1eadt s = \u2212 1 t3 + 9t2, v\u1edbi t (gi\u00e2y) l\u00e0 kho\u1ea3ng th\u1eddi gian t\u00ednh t\u1eeb l\u00fac 2 v\u1eadt b\u1eaft \u0111\u1ea7u chuy\u1ec3n \u0111\u1ed9ng v\u00e0 s (m\u00e9t) l\u00e0 qu\u00e3ng \u0111\u01b0\u1eddng v\u1eadt \u0111i \u0111\u01b0\u1ee3c trong kho\u1ea3ng th\u1eddi gian \u0111\u00f3. H\u1ecfi trong kho\u1ea3ng th\u1eddi gian 10 gi\u00e2y, k\u1ec3 t\u1eeb l\u00fac b\u1eaft \u0111\u1ea7u chuy\u1ec3n \u0111\u1ed9ng, v\u1eadn t\u1ed1c l\u1edbn nh\u1ea5t c\u1ee7a v\u1eadt \u0111\u1ea1t \u0111\u01b0\u1ee3c b\u1eb1ng bao nhi\u00eau ? A 216(m\/s). B 30(m\/s). C 400(m\/s). D 54(m\/s). \u0253 L\u1eddi gi\u1ea3i. V\u1eadn t\u1ed1c t\u1ea1i th\u1eddi \u0111i\u1ec3m t l\u00e0 v(t) = s (t) = \u2212 3 t2 + 18t. 2 Khi \u0111\u00f3 y\u00eau c\u1ea7u b\u00e0i to\u00e1n t\u01b0\u01a1ng \u0111\u01b0\u01a1ng t\u00ecm gi\u00e1 tr\u1ecb l\u1edbn nh\u1ea5t c\u1ee7a h\u00e0m s\u1ed1 y = v(t) = \u2212 3 t2 + 18t tr\u00ean 2 \u0111o\u1ea1n [0; 10] . Ta c\u00f3: y = \u22123t + 18 = 0 \u21d4 t = 6. y(6) = 54; y(0) = 0; y(10) = 30. Do h\u00e0m s\u1ed1 y = v(t) li\u00ean l\u1ee5c tr\u00ean \u0111o\u1ea1n [0; 10] n\u00ean max y = 54. [0;10] Ch\u1ecdn \u0111\u00e1p \u00e1n D \u0104 C\u00e2u 10 (C\u00e2u 7 - \u0110TK - BGD&\u0110T - N\u0103m 2016 - 2017). Cho h\u00e0m s\u1ed1 y = f (x) c\u00f3 b\u1ea3ng bi\u1ebfn thi\u00ean x \u2212\u221e 0 1 +\u221e nh\u01b0 h\u00ecnh v\u1ebd b\u00ean. M\u1ec7nh \u0111\u1ec1 n\u00e0o d\u01b0\u1edbi \u0111\u00e2y y \u22120+0\u2212 \u0111\u00fang? A yC\u0110 = 5. B yCT = 0. +\u221e 5 y C min y = 4. D max y = 5. R R 4 \u2212\u221e \u0253 L\u1eddi gi\u1ea3i. D\u1ef1a v\u00e0o b\u1ea3ng bi\u1ebfn thi\u00ean ta c\u00f3: yC\u0110 = 5, yCT = 4 ch\u1ecdn A. xCT = 0, xC\u0110 = 1 n\u00ean lo\u1ea1i B. H\u00e0m s\u1ed1 kh\u00f4ng c\u00f3 gi\u00e1 tr\u1ecb l\u1edbn nh\u1ea5t v\u00e0 nh\u1ecf nh\u1ea5t tr\u00ean R n\u00ean lo\u1ea1i min y = 4, max y = 5. RR Ch\u1ecdn \u0111\u00e1p \u00e1n A Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t 79 S\u0110T: 0905.193.688","3. Gi\u00e1 tr\u1ecb l\u1edbn nh\u1ea5t v\u00e0 gi\u00e1 tr\u1ecb nh\u1ecf nh\u1ea5t c\u1ee7a h\u00e0m s\u1ed1 \u0104 C\u00e2u 11 (C\u00e2u 23 - M\u0110 101 - BGD&\u0110T - N\u0103m 2017 - 2018). Gi\u00e1 tr\u1ecb l\u1edbn nh\u1ea5t c\u1ee7a h\u00e0m s\u1ed1 y = x4 \u2212 4x2 + 9 tr\u00ean \u0111o\u1ea1n [\u22122; 3] b\u1eb1ng A 201. B 2. C 9. D 54. \u0253 L\u1eddi gi\u1ea3i. H\u00e0m s\u1ed1 \u0111\u00e3 cho x\u00e1c \u0111\u1ecbnh v\u00e0 li\u00ean t\u1ee5c tr\u00ean \u0111o\u1ea1n [\u22122; 3]. Ta c\u00f3 y = 4x3 \u2212 8x. y = 0 \u21d4 4x3 \u2212 8x = 0 \u21d4 \u00f1x = 0 \u2208 [\u22122; 3] \u221a x = \u00b1 2 \u2208 [\u2212\u00c42;\u221a3]. \u00e4 \u00c4\u221a \u00e4 Ta c\u00f3 f (\u22122) = 9, f (3) = 54, f (0) = 9, f \u2212 2 = 5, f 2 = 5. V\u1eady gi\u00e1 tr\u1ecb l\u1edbn nh\u1ea5t c\u1ee7a h\u00e0m s\u1ed1 tr\u00ean \u0111o\u1ea1n [\u22122; 3] b\u1eb1ng f (3) = 54. Ch\u1ecdn \u0111\u00e1p \u00e1n D \u0104 C\u00e2u 12 (C\u00e2u 18 - M\u0110 102 - BGD&\u0110T - N\u0103m 2017 - 2018). Gi\u00e1 tr\u1ecb nh\u1ecf nh\u1ea5t c\u1ee7a h\u00e0m s\u1ed1 y = x3 + 2x2 \u2212 7x tr\u00ean \u0111o\u1ea1n [0; 4] b\u1eb1ng A \u2212259. B 68. C 0. D \u22124. \u0253 L\u1eddi gi\u1ea3i. \uf8eex = 1 (nh\u1eadn) Ta c\u00f3 y = 3x2 + 4x \u2212 7, y = 0 \u21d4 \uf8f0 = \u2212 7 . x (lo\u1ea1i) 4 M\u00e0 y(0) = 0, y(1) = \u22124, y(4) = 68. V\u1eady min y = \u22124. [0;4] Ch\u1ecdn \u0111\u00e1p \u00e1n D \u0104 C\u00e2u 13 (C\u00e2u 21 - M\u0110 103 - BGD&\u0110T - N\u0103m 2017 - 2018). Gi\u00e1 tr\u1ecb nh\u1ecf nh\u1ea5t c\u1ee7a h\u00e0m s\u1ed1 y = x3 + 3x2 tr\u00ean \u0111o\u1ea1n [\u22124; \u22121] b\u1eb1ng A \u22124. B \u221216. C 0. D 4. \u0253 L\u1eddi gi\u1ea3i. Ta c\u00f3 y = 3x2 + 6x; y = 0 \u21d4 3x2 + 6x = 0 \u21d4 \u00f1x = 0 \u2208\/ [\u22124; \u22121] x = \u22122 \u2208 [\u22124; \u22121]. Khi \u0111\u00f3 y(\u22124) = \u221216; y(\u22122) = 4; y(\u22121) = 2 n\u00ean min y = \u221216. [\u22124;\u22121] Ch\u1ecdn \u0111\u00e1p \u00e1n B \u0104 C\u00e2u 14 (C\u00e2u 22 - M\u0110 104 - BGD&\u0110T - N\u0103m 2017 - 2018). Gi\u00e1 tr\u1ecb l\u1edbn nh\u1ea5t c\u1ee7a h\u00e0m s\u1ed1 y = x4 \u2212 x2 + 13 tr\u00ean \u0111o\u1ea1n [\u22121; 2] b\u1eb1ng A 25. B 51 C 13. D 85. . 4 \u0253 L\u1eddi gi\u1ea3i. T\u1eadp x\u00e1c \u0111\u1ecbnh D = R. \uf8eex = 0 \u221a 2 Ta c\u00f3 y = 4x3 \u2212 2x \u21d2 y = 0 \u21d4 \uf8f0 . x=\u00b1 2 \u221a y 2 \u00c7 \u00e5 51 \u00b1 . Khi \u0111\u00f3 y(\u22121) = 13; y(2) = 25; y(0) = 13; = 24 Suy ra gi\u00e1 tr\u1ecb l\u1edbn nh\u1ea5t c\u1ee7a h\u00e0m s\u1ed1 \u0111\u00e3 cho tr\u00ean \u0111o\u1ea1n [\u22121; 2] l\u00e0 25. Ch\u1ecdn \u0111\u00e1p \u00e1n A Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t 80 S\u0110T: 0905.193.688","Ch\u01b0\u01a1ng 1. \u1ee8NG D\u1ee4NG \u0110\u1ea0O H\u00c0M \u0110\u1ec2 KH\u1ea2O S\u00c1T V\u00c0 V\u1ebc \u0110\u1ed2 TH\u1eca C\u1ee6A H\u00c0M S\u1ed0 \u0104 C\u00e2u 15 (C\u00e2u 20 - M\u0110 101 - BGD&\u0110T - N\u0103m 2018 - 2019). Gi\u00e1 tr\u1ecb l\u1edbn nh\u1ea5t c\u1ee7a h\u00e0m s\u1ed1 f (x) = x3 \u2212 3x + 2 tr\u00ean \u0111o\u1ea1n [\u22123; 3] l\u00e0 A \u221216. B 20. C 0. D 4. \u0253 L\u1eddi gi\u1ea3i. H\u00e0m s\u1ed1 f (x) = x3 \u2212 3x + 2 c\u00f3 t\u1eadp x\u00e1c \u0111\u1ecbnh R, f (x) = 3x2 \u2212 3. Cho f (x) = 0 \u21d4 3x2 \u2212 3 = 0 \u21d4 x = \u00b11 \u2208 [\u22123; 3]. Ta c\u00f3 f (1) = 0; f (\u22121) = 4; f (3) = 20; f (\u22123) = \u221216. T\u1eeb \u0111\u00f3 suy ra max f (x) = f (3) = 20. [\u22123;3] Ch\u1ecdn \u0111\u00e1p \u00e1n B \u0104 C\u00e2u 16 (C\u00e2u 17 - M\u0110 102 - BGD&\u0110T - N\u0103m 2018 - 2019). Gi\u00e1 tr\u1ecb nh\u1ecf nh\u1ea5t c\u1ee7a h\u00e0m s\u1ed1 f (x) = x3 \u2212 3x + 2 tr\u00ean \u0111o\u1ea1n [\u22123; 3] b\u1eb1ng A 20. B 4. C 0. D \u221216. \u0253 L\u1eddi gi\u1ea3i. f (x) = 3x2 \u2212 3; f (x) = 0 \u21d4 x = \u00b11 \u2208 [\u22123; 3]. Ta c\u00f3 f (\u22123) = \u221216; f (\u22121) = 4; f (1) = 0; f (3) = 20. \u21d2 min f (x) = \u221216. [\u22123;3] Ch\u1ecdn \u0111\u00e1p \u00e1n D \u0104 C\u00e2u 17 (C\u00e2u 19 - \u0110TK - BGD&\u0110T - l\u1ea7n 1 - N\u0103m 2019 - 2020). Gi\u00e1 tr\u1ecb l\u1edbn nh\u1ea5t c\u1ee7a h\u00e0m s\u1ed1 f (x) = \u2212x4 + 12x2 + 1 tr\u00ean \u0111o\u1ea1n [\u2212 1 ; 2] b\u1eb1ng A 1. B 37. C 33. D 12. \u0253 L\u1eddi gi\u1ea3i. H\u00e0m s\u1ed1 f (x)li\u00ean t\u1ee5c tr\u00ean \u0111o\u1ea1n [\u2212 1 ; 2]. f (x) = \u2212 4x3 + 24x = 4x (\u2212 x2 + 6) \uf8eex = 0 \u2208 (\u22121 ; 2) \u221a f (x) = 0 \u21d4 \uf8efx = \u2212 6 \u2208\/ (\u22121 ; 2) \uf8f0\u221a x = 6 \u2208\/ (\u22121 ; 2) f (\u22121) = 12; f (2) = 33; f (0) = 1. V\u1eady Max f (x) = 33. [\u2212 1 ;2] Ch\u1ecdn \u0111\u00e1p \u00e1n C \u0104 C\u00e2u 18 (C\u00e2u 36 - M\u0110 101 - BGD&\u0110T - \u0110\u1ee3t 1 - N\u0103m 2019 - 2020). Gi\u00e1 tr\u1ecb n\u221ah\u1ecf nh\u1ea5t c\u1ee7a c\u1ee7a h\u00e0m s\u1ed1 f (x) = x3 \u2212 24x tr\u00ean \u0111o\u1ea1\u221an [2; 19] b\u1eb1ng A 32 2. B \u221240. C \u221232 2. D \u221245. \u0253 L\u1eddi gi\u1ea3i. Ta c\u00f3 f (x) = 3x2 \u2212\u221a24. \u00f1x = 2 2 \u2208 [2; 19] f (x) = 0 \u21d4 \u221a x = \u22122 2 \u2208\/ [2; 19].\u221a \u221a f (2) = \u221240; f (19)\u221a= 6043; f (2 2) = \u221232 2. V\u1eady min f (x) = \u221232 2. [2;19] Ch\u1ecdn \u0111\u00e1p \u00e1n C Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t 81 S\u0110T: 0905.193.688","3. Gi\u00e1 tr\u1ecb l\u1edbn nh\u1ea5t v\u00e0 gi\u00e1 tr\u1ecb nh\u1ecf nh\u1ea5t c\u1ee7a h\u00e0m s\u1ed1 \u0104 C\u00e2u 19 (C\u00e2u 35 - M\u0110 103 - BGD&\u0110T - \u0110\u1ee3t 1 - N\u0103m 2019 - 2020). Gi\u00e1 tr\u1ecb n\u221ah\u1ecf nh\u1ea5t c\u1ee7a h\u00e0m s\u1ed1 f (x) = x3 \u2212 30x tr\u00ean \u0111o\u1ea1n [2\u221a; 19] b\u1eb1ng A 20 10. B \u221263. C \u221220 10. D \u221252. \u0253 L\u1eddi gi\u1ea3i. H\u00e0m s\u1ed1 \u0111\u00e3 cho x\u00e1c \u0111\u1ecbnh v\u00e0 li\u00ean t\u1ee5c tr\u00ean \u0111o\u1ea1\u221an [2; 19]. \u00ef x = \u221a10 \u2208 [2; 19] Ta c\u00f3 f (x) = 3x2 \u2212 30; f (x) = 0 \u21d4 x = \u2212 10 \u2208\/ [2; 19] . \u00c4\u221a \u00e4 \u221a M\u00e0 f (2) = \u221252; f 10 = \u221220 10 \u2248 \u221263, 25; f (19) = 6289. \u221a V\u1eady min f (x) = \u221220 10. [2;19] Ch\u1ecdn \u0111\u00e1p \u00e1n C \u0104 C\u00e2u 20 (C\u00e2u 29 - M\u0110 104 - BGD&\u0110T - \u0110\u1ee3t 1 - N\u0103m 2019 - 2020). Gi\u00e1 tr\u1ecb nh\u1ecf nh\u1ea5t c\u1ee7a h\u00e0m s\u1ed1 f (x) \u221a= x3 \u2212 33x tr\u00ean \u0111o\u1ea1n [2; 19] b\u1eb1ng \u221a A \u221272. B \u221222 11. C \u221258. D 22 11. \u0253 L\u1eddi gi\u1ea3i. Ta c\u00f3 f (x) = 3x2 \u2212 33. \u221a f (x) = 0 \u21d4 x2 = 11 \u21d4 x \u221a= \u00b1 11. X\u00e9t tr\u00ean [2; 19] ta c\u00f3 \u00c4x\u221a= 11 \u2208 [2;\u221a19]. Ta c\u00f3 f (2) = \u221258; f \u00e4 \u221222 11; 11 = f (19) = 6232. \u00c4\u221a \u00e4 \u221a V\u1eady min f (x) = f 11 = \u221222 11. [2;19] Ch\u1ecdn \u0111\u00e1p \u00e1n B \u0104 C\u00e2u 21 (C\u00e2u 31 - M\u0110 101 - BGD&\u0110T - \u0110\u1ee3t 2 - N\u0103m 2019 - 2020). Gi\u00e1 tr\u1ecb nh\u1ecf nh\u1ea5t c\u1ee7a h\u00e0m s\u1ed1 f (x) = x4 \u2212 10x2 \u2212 4 tr\u00ean \u0111o\u1ea1n [0; 9] b\u1eb1ng A \u221228. B \u22124. C \u221213. D \u221229. \u0253 L\u1eddi gi\u1ea3i. Ta c\u00f3 f (x) = 4x3 \u2212 20x = 4x(x2 \u2212 5) = 0, f (x) = 0 \u21d4 \u00f1x = 0 \u221a x = \u00b1\u221a 5. Nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh f\u221a(x) = 0 tr\u00ean kho\u1ea3ng (0; 9) l\u00e0 x = 5. Ta t\u00ednh \u0111\u01b0\u1ee3c f (0) = \u22124, f ( 5) = \u221229 v\u00e0 f (9) = 5747. V\u1eady gi\u00e1 tr\u1ecb nh\u1ecf nh\u1ea5t c\u1ea7n t\u00ecm l\u00e0 \u221229. Ch\u1ecdn \u0111\u00e1p \u00e1n D \u0104 C\u00e2u 22 (C\u00e2u 32 - M\u0110 102 - BGD&\u0110T - \u0110\u1ee3t 2 - N\u0103m 2019 - 2020). Gi\u00e1 tr\u1ecb nh\u1ecf nh\u1ea5t c\u1ee7a h\u00e0m s\u1ed1 f (x) = x4 \u2212 12x2 \u2212 4 tr\u00ean \u0111o\u1ea1n [0; 9] b\u1eb1ng A \u221239. B \u221240. C \u221236. D \u22124. \u0253 L\u1eddi gi\u1ea3i. \uf8eex = 0 \u221a \u2022 Ta c\u00f3 f (x) = 4x3 \u2212 24x; f (x) = 0 \u21d4 \uf8efx = 6 \uf8f0\u221a x\u221a= \u2212 6 (lo\u1ea1i). \u2022 T\u00ednh \u0111\u01b0\u1ee3c f (0) = \u22124; f (9) = 5585 v\u00e0 f ( 6) = \u221240. \u2022 Do \u0111\u00f3 min f (x) = \u221240. [0;9] Ch\u1ecdn \u0111\u00e1p \u00e1n B Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t 82 S\u0110T: 0905.193.688","Ch\u01b0\u01a1ng 1. \u1ee8NG D\u1ee4NG \u0110\u1ea0O H\u00c0M \u0110\u1ec2 KH\u1ea2O S\u00c1T V\u00c0 V\u1ebc \u0110\u1ed2 TH\u1eca C\u1ee6A H\u00c0M S\u1ed0 \u0104 C\u00e2u 23 (C\u00e2u 32 - M\u0110 103 - BGD&\u0110T - \u0110\u1ee3t 2 - N\u0103m 2019 - 2020). Gi\u00e1 tr\u1ecb nh\u1ecf nh\u1ea5t c\u1ee7a h\u00e0m s\u1ed1 f (x) = x4 \u2212 10x2 \u2212 2 tr\u00ean \u0111o\u1ea1n [0; 9] b\u1eb1ng A \u22122. B \u221211. C \u221226. D \u221227. \u0253 L\u1eddi gi\u1ea3i. Ta c\u00f3 f (x) = 4x3 \u2212 20x = 4x(x2 \u2212 5) = 0, f (x) = 0 \u21d4 \u00f1x = 0 \u221a x = \u00b1\u221a 5. Nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh f\u221a(x) = 0 tr\u00ean kho\u1ea3ng (0; 9) l\u00e0 x = 5. Ta t\u00ednh \u0111\u01b0\u1ee3c f (0) = \u22122, f ( 5) = \u221227 v\u00e0 f (9) = 5745. V\u1eady gi\u00e1 tr\u1ecb nh\u1ecf nh\u1ea5t c\u1ea7n t\u00ecm l\u00e0 \u221227. Ch\u1ecdn \u0111\u00e1p \u00e1n D \u0104 C\u00e2u 24 (C\u00e2u 31 - M\u0110 102 - BGD&\u0110T - \u0110\u1ee3t 4 - N\u0103m 2019 - 2020). Gi\u00e1 tr\u1ecb nh\u1ecf nh\u1ea5t c\u1ee7a h\u00e0m s\u1ed1 f (x) = x4 \u2212 12x2 \u2212 1 tr\u00ean \u0111o\u1ea1n [0; 9] b\u1eb1ng A \u221228. B \u22121. C \u221236. D \u221237. \u0253 L\u1eddi gi\u1ea3i. \uf8eex = 0 \u221a Tr\u00ean \u0111o\u1ea1n [0; 9], ta c\u00f3 f (x) = 4x3 \u2212 24x \u21d2 y = 0 \u21d4 4x3 \u2212 24x = 0 \u21d4 \uf8efx = \u2212 6 \u2208\/ [0; 9] \uf8f0\u221a x = 6. \u00c4\u221a \u00e4 Ta c\u00f3 f (0) = \u22121, f 6 = \u221237, f (9) = 5588. \u221a\u00e4 V\u1eady gi\u00e1 tr\u1ecb nh\u1ecf nh\u1ea5t c\u1ee7a h\u00e0m s\u1ed1 f (x) = x4 \u2212 12x2 \u2212 1 tr\u00ean \u0111o\u1ea1n [0; 9] l\u00e0 \u221237 \u00c4 x = 6. t\u1ea1i Ch\u1ecdn \u0111\u00e1p \u00e1n D \u0104 C\u00e2u 25 (C\u00e2u 31 - M\u0110 101 - BGD&\u0110T - \u0110\u1ee3t 1 - N\u0103m 2020 - 2021). Tr\u00ean \u0111o\u1ea1n [0; 3], h\u00e0m s\u1ed1 y = \u2212x3 + 3x \u0111\u1ea1t gi\u00e1 tr\u1ecb l\u1edbn nh\u1ea5t t\u1ea1i \u0111i\u1ec3m A x = 0. B x = 3. C x = 1. D x = 2. \u0253 L\u1eddi gi\u1ea3i. X\u00e9t h\u00e0m s\u1ed1 f (x) = \u2212x3 + 3x tr\u00ean [0; 3]. Ta c\u00f3 f (x) = \u22123x2 + 3, y \u00f1x = 1 =0\u21d4 x = \u22121 \u2208\/ [0; 3]. Ta c\u00f3 f (0) = 0; f (1) = 2; f (3) = \u221218 \u21d2 max f (x) = f (1) = 2. [0;3] V\u1eady h\u00e0m s\u1ed1 y = \u2212x3 + 3x \u0111\u1ea1t gi\u00e1 tr\u1ecb l\u1edbn nh\u1ea5t tr\u00ean [0; 3] t\u1ea1i x = 1. Ch\u1ecdn \u0111\u00e1p \u00e1n C \u0104 C\u00e2u 26 (C\u00e2u 35 - M\u0110 102 - BGD&\u0110T - \u0110\u1ee3t 1 - N\u0103m 2020 - 2021). Tr\u00ean \u0111o\u1ea1n [\u22122; 1], h\u00e0m s\u1ed1 y = x3 \u2212 3x2 \u2212 1 \u0111\u1ea1t gi\u00e1 tr\u1ecb l\u1edbn nh\u1ea5t t\u1ea1i \u0111i\u1ec3m A x = \u22122. B x = 0. C x = \u22121. D x = 1. \u0253 L\u1eddi gi\u1ea3i. H\u00e0m s\u1ed1 y = x3 \u2212 3x2 \u2212 1 x\u00e1c \u0111\u1ecbnh v\u00e0 li\u00ean t\u1ee5c tr\u00ean \u0111o\u1ea1n [\u22122; 1], c\u00f3 y = 3x2 \u2212 6x. Ta c\u00f3 y = 0 \u21d4 3x2 \u2212 6x = 0 \u21d4 \u00f1x = 0 \u2208 [\u22122; 1] x = 2 \u2208\/ [\u22122; 1]. M\u00e0 y(\u22122) = \u221221, y(0) = \u22121, y(1) = \u22123 n\u00ean h\u00e0m s\u1ed1 c\u00f3 gi\u00e1 tr\u1ecb l\u1edbn nh\u1ea5t b\u1eb1ng \u22121 t\u1ea1i x = 0. Ch\u1ecdn \u0111\u00e1p \u00e1n B Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t 83 S\u0110T: 0905.193.688","3. Gi\u00e1 tr\u1ecb l\u1edbn nh\u1ea5t v\u00e0 gi\u00e1 tr\u1ecb nh\u1ecf nh\u1ea5t c\u1ee7a h\u00e0m s\u1ed1 \u0104 C\u00e2u 27 (C\u00e2u 37 - M\u0110 104 - BGD&\u0110T - \u0110\u1ee3t 1 - N\u0103m 2020 - 2021). Tr\u00ean \u0111o\u1ea1n [\u22121; 2], h\u00e0m s\u1ed1 y = x3 + 3x2 + 1 \u0111\u1ea1t gi\u00e1 tr\u1ecb nh\u1ecf nh\u1ea5t t\u1ea1i \u0111i\u1ec3m A x = 2. B x = 0. C x = \u22121. D x = 1. \u0253 L\u1eddi gi\u1ea3i. H\u00e0m s\u1ed1 y = x3 + 3x2 + 1 li\u00ean t\u1ee5c tr\u00ean \u0111o\u1ea1n [\u22121; 2]. Ta c\u00f3 y = 3x2 + 6x. \u00f1x = 0 \u2208 [\u22121; 2] Cho y = 0 \u21d4 x = \u22122 \u2208\/ [\u22121; 2]. Khi x = 0 \u21d2 y = 1. Khi x = \u22121 \u21d2 y = 3. Khi x = 2 \u21d2 y = 13. V\u1eady tr\u00ean \u0111o\u1ea1n [\u22121; 2] h\u00e0m s\u1ed1 \u0111\u1ea1t gi\u00e1 tr\u1ecb nh\u1ecf nh\u1ea5t t\u1ea1i \u0111i\u1ec3m x = 0. Ch\u1ecdn \u0111\u00e1p \u00e1n B \u0104 C\u00e2u 28 (C\u00e2u 34 - M\u0110 102 - BGD&\u0110T - \u0110\u1ee3t 2 - N\u0103m 2020 - 2021). Tr\u00ean \u0111o\u1ea1n [\u22124; \u22121], h\u00e0m s\u1ed1 y = \u2212x4 + 8x2 \u2212 19 \u0111\u1ea1t gi\u00e1 tr\u1ecb l\u1edbn nh\u1ea5t t\u1ea1i \u0111i\u1ec3m A x = \u22123. B x = \u22122. C x = \u22124. D x = \u22121. \u0253 L\u1eddi gi\u1ea3i. Ta c\u00f3 y = \u22124x3 + 16x = \u22124x (x2 \u2212 4). \uf8eex = 0 \u2208\/ [\u22124; \u22121] X\u00e9t y = 0 \u21d4 \uf8efx = 2 \u2208\/ [\u22124; \u22121] \uf8f0 x = \u22122 \u2208 [\u22124; \u22121]. Ta c\u00f3 y(\u22124) = \u2212147, y(\u22122) = \u22123 v\u00e0 y(\u22121) = \u221212. V\u1eady max y = \u22123 khi x = \u22122. [\u22124;\u22121] Ch\u1ecdn \u0111\u00e1p \u00e1n B \u0104 C\u00e2u 29 (C\u00e2u 30 - M\u0110 103 - BGD&\u0110T - \u0110\u1ee3t 2 - N\u0103m 2020 - 2021). Tr\u00ean \u0111o\u1ea1n [1; 4], h\u00e0m s\u1ed1 y = x4 \u2212 8x2 + 19 \u0111\u1ea1t gi\u00e1 tr\u1ecb nh\u1ecf nh\u1ea5t t\u1ea1i \u0111i\u1ec3m A x = 2. B x = 1. C x = 3. D x = 4. \u0253 L\u1eddi gi\u1ea3i. H\u00e0m s\u1ed1 y = x4 \u2212 8x2 + 19 li\u00ean t\u1ee5c tr\u00ean \u0111o\u1ea1n [1; 4]. Ta c\u00f3 y = 4x3 \u2212 16x. \uf8eex = 0 \u2208\/ [1; 4] y = 0 \u21d4 4x3 \u2212 16x = 0 \u21d4 \uf8efx = \u22122 \u2208\/ [1; 4] \uf8f0 x = 2 \u2208 [1; 4]. Ta t\u00ednh \u0111\u01b0\u1ee3c y(1) = 12, y(2) = 3, y(4) = 147. V\u1eady h\u00e0m s\u1ed1 \u0111\u00e3 cho \u0111\u1ea1t gi\u00e1 tr\u1ecb nh\u1ecf nh\u1ea5t tr\u00ean \u0111o\u1ea1n [1; 4] l\u00e0 min y = 3 t\u1ea1i \u0111i\u1ec3m x = 2. x\u2208[1;4] Ch\u1ecdn \u0111\u00e1p \u00e1n A \u0104 C\u00e2u 30 (C\u00e2u 35 - M\u0110 104 - BGD&\u0110T - \u0110\u1ee3t 2 - N\u0103m 2020 - 2021). Tr\u00ean \u0111o\u1ea1n [1; 4], h\u00e0m s\u1ed1 y = \u2212x4 + 8x2 \u2212 13 \u0111\u1ea1t gi\u00e1 tr\u1ecb l\u1edbn nh\u1ea5t t\u1ea1i \u0111i\u1ec3m A x = 4. B x = 2. C x = 1. D x = 3. Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t 84 S\u0110T: 0905.193.688","Ch\u01b0\u01a1ng 1. \u1ee8NG D\u1ee4NG \u0110\u1ea0O H\u00c0M \u0110\u1ec2 KH\u1ea2O S\u00c1T V\u00c0 V\u1ebc \u0110\u1ed2 TH\u1eca C\u1ee6A H\u00c0M S\u1ed0 \u0253 L\u1eddi gi\u1ea3i. T\u1eadp x\u00e1c \u0111\u1ecbnh D = R. \uf8eex = \u22122 \u2208\/ [1; 4] Ta c\u00f3 y = \u22124x3 + 16x = 0 \u21d4 \uf8efx = 0 \u2208\/ [1; 4] \uf8f0 x = 2 \u2208 [1; 4]. H\u00e0m s\u1ed1 \u0111\u00e3 cho li\u00ean t\u1ee5c tr\u00ean \u0111o\u1ea1n [1; 4] v\u00e0 ta t\u00ednh \u0111\u01b0\u1ee3c y(1) = \u22126; y(2) = 5 v\u00e0 y(4) = \u2212141. V\u1eady tr\u00ean \u0111o\u1ea1n [1; 4] h\u00e0m s\u1ed1 \u0111\u00e3 cho \u0111\u1ea1t gi\u00e1 tr\u1ecb l\u1edbn nh\u1ea5t l\u00e0 5 t\u1ea1i \u0111i\u1ec3m x = 2. Ch\u1ecdn \u0111\u00e1p \u00e1n B \u0104 C\u00e2u 31 (C\u00e2u 30 - M\u0110 101 - BGD&\u0110T - N\u0103m 2021 - 2022). Gi\u00e1 tr\u1ecb l\u1edbn nh\u1ea5t c\u1ee7a h\u00e0m s\u1ed1 f (x) = x3 \u2212 3x2 \u2212 9x + 10 tr\u00ean \u0111o\u1ea1n [\u22122; 2] b\u1eb1ng A \u221212. B 10. C 15. D \u22122. \u0253 L\u1eddi gi\u1ea3i. X\u00e9t h\u00e0m s\u1ed1 f (x) = x3 \u2212 3x2 \u2212 9x + 10 tr\u00ean \u0111o\u1ea1n [\u22122; 2], ta c\u00f3 f (x) = 3x2 \u2212 6x \u2212 9. f (x) = 0 \u21d4 3x2 \u2212 6x \u2212 9 = 0 \u21d4 \u00f1x = \u22121 \u2208 [\u22122; 2] x = 3 \u2208\/ [\u22122; 2]. f (\u22122) = 8; f (\u22121) = 15; f (2) = \u221212. Suy ra max f (x) = f (\u22121) = 15. [\u22122;2] Ch\u1ecdn \u0111\u00e1p \u00e1n C \u0104 C\u00e2u 32 (C\u00e2u 31 - M\u0110 102 - BGD&\u0110T - N\u0103m 2021 - 2022). Gi\u00e1 tr\u1ecb tr\u1ecb l\u1edbn nh\u1ea5t c\u1ee7a h\u00e0m s\u1ed1 f (x) = x3 \u2212 3x2 \u2212 9x + 10 tr\u00ean \u0111o\u1ea1n [\u22122; 2] b\u1eb1ng A 15. B 10. C \u22121. D \u221212. \u0253 L\u1eddi gi\u1ea3i. Ta c\u00f3 f (x) = 3x2 \u2212 6x \u2212 9; \u00aef (x) = 0 \uf8f1 \u00f1x = \u22121 \uf8f4 \uf8f2 \u21d4 x = 3 \u21d4 x = \u22121; x \u2208 (\u22122; 2) \uf8f4\uf8f3x \u2208 (\u22122; 2) f (\u22122) = 8, f (\u22121) = 15, f (2) = \u221212. V\u1eady max f (x) = f (\u22121) = 15. [\u22122;2] Ch\u1ecdn \u0111\u00e1p \u00e1n A \u0104 C\u00e2u 33 (C\u00e2u 40 - M\u0110 104 - BGD&\u0110T - N\u0103m 2021 - 2022). Cho h\u00e0m s\u1ed1 f (x) = (a + 3)x4 \u2212 2ax2 + 1 v\u1edbi a l\u00e0 tham s\u1ed1 th\u1ef1c. N\u1ebfu max f (x) = f (2) th\u00ec min f (x) [0;3] [0;3] b\u1eb1ng A \u22129. B 4. C 1. D \u22128. \u0253 L\u1eddi gi\u1ea3i. X\u00e9t h\u00e0m f (x) = (a + 3)x4 \u2212 2ax2 + 1 \u21d2 f (x) = 4(a + 3)x3 \u2212 4ax. H\u00e0m s\u1ed1 \u0111\u1ea1t GTLN t\u1ea1i x = 2 v\u00e0 li\u00ean t\u1ee5c tr\u00ean \u0111o\u1ea1n [0; 3]. Do \u0111\u00f3 f (2) = 0 \u21d4 32(a + 3) \u2212 8a = 0 \u21d4 a = \u22124. V\u1edbi a = \u22124 ta c\u00f3 f (x) = \u2212x4 + 8x2 + 1 v\u1edbi x \u2208 [0; 3]. Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t 85 S\u0110T: 0905.193.688","3. Gi\u00e1 tr\u1ecb l\u1edbn nh\u1ea5t v\u00e0 gi\u00e1 tr\u1ecb nh\u1ecf nh\u1ea5t c\u1ee7a h\u00e0m s\u1ed1 \uf8eex = 0 (th\u1ecfa m\u00e3n) f (x) = \u22124x3 + 16x Cho f (x) = 0 \u21d4 \uf8ef\uf8f0x = 2 (th\u1ecfa m\u00e3n) x = \u22122 (lo\u1ea1i). Khi \u0111\u00f3 f (0) = 1, f (2) = 17, f (3) = \u22128. Suy ra max f (x) = f (2) = 17 (th\u1ecfa m\u00e3n gi\u1ea3 thi\u1ebft). [0;3] V\u1eady min f (x) = f (3) = \u22128. [0;3] Ch\u1ecdn \u0111\u00e1p \u00e1n D \u0104 C\u00e2u 34 (C\u00e2u 29 - \u0110MH - BGD&\u0110T - N\u0103m 2021 - 2022). 4 Tr\u00ean \u0111o\u1ea1n [1; 5], h\u00e0m s\u1ed1 y = x + \u0111\u1ea1t gi\u00e1 tr\u1ecb nh\u1ecf nh\u1ea5t t\u1ea1i \u0111i\u1ec3m x A x = 5. B x = 2. C x = 1. D x = 4. \u0253 L\u1eddi gi\u1ea3i. Ta c\u00f3 y = 1 \u2212 4 = x2 \u2212 4 = 0 \u21d4 \u00f1x = 2 (nh\u1eadn) x2 x2 x = \u22122 (lo\u1ea1i). 4 f (1) = 1 + = 5. 1 4 f (2) = 2 + = 4. 2 4 29 f (5) = 5 + = . 55 V\u1eady gi\u00e1 tr\u1ecb nh\u1ecf nh\u1ea5t c\u1ee7a h\u00e0m s\u1ed1 l\u00e0 4 t\u1ea1i \u0111i\u1ec3m x = 2. Ch\u1ecdn \u0111\u00e1p \u00e1n B \u0104 C\u00e2u 35 (C\u00e2u 19 - \u0110TK - BGD&\u0110T - N\u0103m 2016 - 2017). 4 T\u00ednh gi\u00e1 tr\u1ecb nh\u1ecf nh\u1ea5t c\u1ee7a h\u00e0m s\u1ed1 y = 3x + tr\u00ean kho\u1ea3ng (0; +\u221e). x2 \u221a B min y = 7. C 33 \u221a A min y = 3 3 9. min y = . D min y = 2 3 9. (0;+\u221e) (0;+\u221e) (0;+\u221e) 5 (0;+\u221e) \u0253 L\u1eddi gi\u1ea3i. Ta c\u00f3 y =3\u2212 8 3x3 \u2212 8 = 0 \u21d4 3x3 \u2212 8 = 0 \u21d4 x = \u2026 8 . Ta c\u00f3 b\u1ea3ng bi\u1ebfn thi\u00ean: = ;y 3 x3 x3 3 x0 \u2026 8 +\u221e 3 3 y \u22120+ +\u221e +\u221e y \u221a 339 Ch\u1ecdn \u0111\u00e1p \u00e1n A \u221a T\u1eeb b\u1ea3ng bi\u1ebfn thi\u00ean suy ra: min y = 3 3 9. (0;+\u221e) Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t 86 S\u0110T: 0905.193.688","Ch\u01b0\u01a1ng 1. \u1ee8NG D\u1ee4NG \u0110\u1ea0O H\u00c0M \u0110\u1ec2 KH\u1ea2O S\u00c1T V\u00c0 V\u1ebc \u0110\u1ed2 TH\u1eca C\u1ee6A H\u00c0M S\u1ed0 \u0104 C\u00e2u 36 (C\u00e2u 17 - M\u0110 101 - BGD&\u0110T - N\u0103m 2017 - 2018). Cho h\u00e0m s\u1ed1 f (x) = ax3 + bx2 + cx + d (a, b, c, d \u2208 R). \u0110\u1ed3 th\u1ecb c\u1ee7a h\u00e0m s\u1ed1 y 2 y = f (x) nh\u01b0 h\u00ecnh v\u1ebd b\u00ean. S\u1ed1 nghi\u1ec7m th\u1ef1c c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh 3f (x)+4 = 0 O l\u00e0 A 3. B 0. C 1. D 2. 2 x \u22122 \u0253 L\u1eddi gi\u1ea3i. Ta c\u00f3 3f (x) + 4 = 0 \u21d4 f (x) = \u22124 . 3 D\u1ef1a v\u00e0o \u0111\u1ed3 th\u1ecb, \u0111\u01b0\u1eddng th\u1eb3ng y = \u22124 c\u1eaft \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 y = f (x) t\u1ea1i ba \u0111i\u1ec3m ph\u00e2n bi\u1ec7t. 3 Ch\u1ecdn \u0111\u00e1p \u00e1n A \u0104 C\u00e2u 37 (C\u00e2u 23 - M\u0110 101 - BGD&\u0110T - N\u0103m 2016 - 2017). T\u00ecm gi\u00e1 tr\u1ecb nh\u1ecf nh\u1ea5t m c\u1ee7a h\u00e0m s\u1ed1 y = x3 \u2212 7x2 + 11x \u2212 2 tr\u00ean \u0111o\u1ea1n [0; 2]. A m = 11. B m = 0. C m = \u22122. D m = 3. \u0253 L\u1eddi gi\u1ea3i. \u0110\u1ea1o h\u00e0m: y = 3x2 \u2212 14x + 11 c\u00f3 nghi\u1ec7m x = 1 \u2208 [0; 2]. Ta c\u00f3 y(0) = \u22122; y(1) = 3; y(2) = 0 \u21d2 m = min y = \u22122. [0;2] Ch\u1ecdn \u0111\u00e1p \u00e1n C \u0104 C\u00e2u 38 (C\u00e2u 20 - M\u0110 104 - BGD&\u0110T - N\u0103m 2016 - 2017). T\u00ecm gi\u00e1 tr\u1ecb nh\u1ecf nh\u1ea5t m c\u1ee7a h\u00e0m s\u1ed1 y = x2 + 2 tr\u00ean \u0111o\u1ea1n \u00ef1 \u00f2 ;2 . x2 A m= 17 B m = 10. C m = 5. D m = 3. . 4 \u0253 L\u1eddi gi\u1ea3i. 2 2x3 \u2212 2 T\u1eadp x\u00e1c \u0111\u1ecbnh D = R \\\\ {0}. Ta c\u00f3 y = 2x \u2212 x2 = x2 . B\u1ea3ng bi\u1ebfn thi\u00ean: x 1 1 2 2 y \u22120+ 17 5 y4 3 Ch\u1ecdn \u0111\u00e1p \u00e1n D \u0104 C\u00e2u 39 (C\u00e2u 40 - M\u0110 101 - BGD&\u0110T - N\u0103m 2021 - 2022). Cho h\u00e0m s\u1ed1 f (x) = (m \u2212 1)x4 \u2212 2mx2 + 1 v\u1edbi m l\u00e0 tham s\u1ed1 th\u1ef1c. N\u1ebfu min f (x) = f (2) th\u00ec [0;3] max f (x) b\u1eb1ng [0;3] Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t 87 S\u0110T: 0905.193.688","3. Gi\u00e1 tr\u1ecb l\u1edbn nh\u1ea5t v\u00e0 gi\u00e1 tr\u1ecb nh\u1ecf nh\u1ea5t c\u1ee7a h\u00e0m s\u1ed1 A \u221213. B 4. C \u221214. D 1. 3 3 \u0253 L\u1eddi gi\u1ea3i. Ta c\u00f3 f (x) = (m \u2212 1)x4 \u2212 2mx2 + 1 n\u00ean f (x) = 4(m \u2212 1)x3 \u2212 4mx = 4x [(m \u2212 1)x2 \u2212 m]. Do \u0111\u00f3 \u00f1x = 0 f (x) = 0 \u21d4 (m \u2212 1)x2 \u2212 m = 0. (\u2217) \u0110i\u1ec1u ki\u1ec7n c\u1ea7n \u0111\u1ec3 min f (x) = f (2) l\u00e0 ph\u01b0\u01a1ng tr\u00ecnh (\u2217) c\u00f3 nghi\u1ec7m x = 2 [0;3] T\u01b0\u01a1ng \u0111\u01b0\u01a1ng 4(m \u2212 1) \u2212 m = 0 \u21d4 m = 4 \u00b7 3 1 8 4 16 Khi \u0111\u00f3 f (x) = 3 x4 \u2212 3 x2 + 1 \u21d2 f (x) = 3 x3 \u2212 3 x. \uf8eex = 0 \u2208 [0; 3] Ta c\u00f3 f (x) = 0 \u21d4 \uf8efx = 2 \u2208 [0; 3] \uf8f0 x = \u22122 \u2208\/ [0; 3]. Ta c\u00f3 f (0) = 1; f (3) = 4; f (2) = \u2212 13 \u00b7 3 13 V\u1eady min f (x) = f (2) = \u2212 3 v\u00e0 max f (x) = 4 khi x = 3. [0;3] [0;3] Ch\u1ecdn \u0111\u00e1p \u00e1n B \u0104 C\u00e2u 40 (C\u00e2u 39 - M\u0110 102 - BGD&\u0110T - N\u0103m 2021 - 2022). Cho h\u00e0m s\u1ed1 f (x) = mx4 + 2(m \u2212 1)x2 v\u1edbi m l\u00e0 tham s\u1ed1 th\u1ef1c. N\u1ebfu min f (x) = f (1) th\u00ec max f (x) [0;2] [0;2] b\u1eb1ng A 2. B \u22121. C 4. D 0. \u0253 L\u1eddi gi\u1ea3i. Ta c\u00f3 f (x) = 4mx3 + 4(m \u2212 1)x. V\u1edbi m = 0 th\u00ec f (x) = \u22122x2 l\u00e0 h\u00e0m s\u1ed1 ngh\u1ecbch bi\u1ebfn tr\u00ean (0; 2). Khi \u0111\u00f3 min f (x) = f (2) (kh\u00f4ng th\u1ecfa y\u00eau c\u1ea7u b\u00e0i to\u00e1n). [0;2] V\u1edbi m = 0 th\u00ec h\u00e0m s\u1ed1 y = f (x) c\u00f3 \u0111\u1ed3 th\u1ecb nh\u1eadn Oy l\u00e0m tr\u1ee5c \u0111\u1ed1i x\u1ee9ng v\u00e0 lu\u00f4n c\u00f3 m\u1ed9t \u0111i\u1ec3m c\u1ef1c tr\u1ecb x = 0. Khi \u0111\u00f3, t\u1eeb y\u00eau c\u1ea7u b\u00e0i to\u00e1n ta suy ra \u00aem > 0 \u21d4 \u00aem > 0 \u21d4 m = 1\u00b7 f (1) = 0 4m + 4(m \u2212 1) = 0 2 \uf8eex = \u22121 \u2208\/ (0; 2) Do \u0111\u00f3 f (x) = 2x3 \u2212 2x; f (x) = 0 \u21d4 \uf8efx = 0 \u2208\/ (0; 2) \uf8f0 x = 1 \u2208 (0; 2). Ta c\u00f3 f (0) = 0, f (2) = 4, f (1) = \u22121 \u00b7 2 V\u1eady max f (x) = 4 t\u1ea1i x = 2. [0;2] Ch\u1ecdn \u0111\u00e1p \u00e1n C \u0104 C\u00e2u 41 (C\u00e2u 40 - M\u0110 103 - BGD&\u0110T - N\u0103m 2021 - 2022). Cho h\u00e0m s\u1ed1 f (x) = ax4 + 2(a + 4)x2 \u2212 1 v\u1edbi a l\u00e0 tham s\u1ed1 th\u1ef1c. N\u1ebfu maxf (x) = f (1) th\u00ec minf (x) [0;2] [0;2] b\u1eb1ng A \u221217. B \u221216. C \u22121. D 3. Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t 88 S\u0110T: 0905.193.688","Ch\u01b0\u01a1ng 1. \u1ee8NG D\u1ee4NG \u0110\u1ea0O H\u00c0M \u0110\u1ec2 KH\u1ea2O S\u00c1T V\u00c0 V\u1ebc \u0110\u1ed2 TH\u1eca C\u1ee6A H\u00c0M S\u1ed0 \u0253 L\u1eddi gi\u1ea3i. T\u1eeb gi\u1ea3 thi\u1ebft ta c\u00f3 f (1) = 0 \u21d2 4a + 4(a + 4) = 0 \u21d4 a = \u22122 v\u00e0 f (x) = \u22122x4 + 4x2 \u2212 1. Ta c\u00f3 f (0) = \u22121, f (1) = 1, f (2) = \u221217. V\u1eady min f (x) = f (2) = \u221217 [0;2] Ch\u1ecdn \u0111\u00e1p \u00e1n A \u0104 C\u00e2u 42 (C\u00e2u 10 - \u0110MH - BGD&\u0110T - N\u0103m 2016 - 2017). Cho m\u1ed9t t\u1ea5m nh\u00f4m h\u00ecnh vu\u00f4ng c\u1ea1nh 12 cm. Ng\u01b0\u1eddi ta c\u1eaft \u1edf b\u1ed1n g\u00f3c c\u1ee7a t\u1ea5m nh\u00f4m \u0111\u00f3 b\u1ed1n h\u00ecnh vu\u00f4ng b\u1eb1ng nhau, m\u1ed7i h\u00ecnh vu\u00f4ng c\u00f3 c\u1ea1nh b\u1eb1ng x cm, r\u1ed3i g\u1eadp t\u1ea5m nh\u00f4m l\u1ea1i nh\u01b0 h\u00ecnh v\u1ebd d\u01b0\u1edbi \u0111\u00e2y \u0111\u1ec3 \u0111\u01b0\u1ee3c m\u1ed9t c\u00e1i h\u1ed9p kh\u00f4ng n\u1eafp. T\u00ecm x \u0111\u1ec3 h\u1ed9p nh\u1eadn \u0111\u01b0\u1ee3c c\u00f3 th\u1ec3 t\u00edch l\u1edbn nh\u1ea5t. A x = 6. B x = 3. C x = 2. D x = 4. \u0253 L\u1eddi gi\u1ea3i. M\u1eb7t \u0111\u00e1y c\u1ee7a h\u1ed9p l\u00e0 h\u00ecnh vu\u00f4ng c\u00f3 c\u1ea1nh b\u1eb1ng 12 \u2212 2x (cm), v\u1edbi 0 < x < 6. V\u1eady di\u1ec7n t\u00edch c\u1ee7a \u0111\u00e1y h\u1ed9p l\u00e0 S = (12 \u2212 2x)2 = 4(6 \u2212 x)2. Kh\u1ed1i h\u1ed9p c\u00f3 chi\u1ec1u cao h = x (cm). V\u1eady th\u1ec3 t\u00edch h\u1ed9p l\u00e0 V = S \u00b7 h = 4(6 \u2212 x)2 \u00b7 x = 4x3 \u2212 48x2 + 144x (cm3). X\u00e9t h\u00e0m f (x) = 4x3 \u2212 48x2 + 144x, 0 < x < 6. Ta c\u00f3 f (x) = 12x2 \u2212 96x + 144 \u21d2 f (x) = 0 \u21d4 x2 \u2212 8x + 12 = 0 \u21d4 \u00f1x = 2 . x=6 Do 0 < x < 6 n\u00ean ta l\u1ea5y x = 2. Ta c\u00f3 b\u1ea3ng bi\u1ebfn thi\u00ean: x0 2 6 f +0\u2212 128 f 00 V\u1eady th\u1ec3 t\u00edch kh\u1ed1i h\u1ed9p \u0111\u1ea1t gi\u00e1 tr\u1ecb l\u1edbn nh\u1ea5t khi x = 2 (cm). Ch\u1ecdn \u0111\u00e1p \u00e1n C \u0104 C\u00e2u 43 (C\u00e2u 30 - M\u0110 103 - BGD&\u0110T - N\u0103m 2017 - 2018). \u00d4ng A d\u1ef1 \u0111\u1ecbnh s\u1eed d\u1ee5ng h\u1ebft 5 m2 k\u00ednh \u0111\u1ec3 l\u00e0m m\u1ed9t b\u1ec3 c\u00e1 b\u1eb1ng k\u00ednh c\u00f3 d\u1ea1ng h\u00ecnh h\u1ed9p ch\u1eef nh\u1eadt kh\u00f4ng n\u1eafp, chi\u1ec1u d\u00e0i g\u1ea5p \u0111\u00f4i chi\u1ec1u r\u1ed9ng (c\u00e1c m\u1ed1i gh\u00e9p c\u00f3 k\u00edch th\u01b0\u1edbc kh\u00f4ng \u0111\u00e1ng k\u1ec3). B\u1ec3 c\u00e1 c\u00f3 dung t\u00edch l\u1edbn nh\u1ea5t b\u1eb1ng bao nhi\u00eau (k\u1ebft qu\u1ea3 l\u00e0m tr\u00f2n \u0111\u1ebfn h\u00e0ng ph\u1ea7n tr\u0103m)? A 1,01 m3. B 0,96 m3. C 1,33 m3. D 1,51 m3. Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t \u0253 L\u1eddi gi\u1ea3i. S\u0110T: 0905.193.688 89","3. Gi\u00e1 tr\u1ecb l\u1edbn nh\u1ea5t v\u00e0 gi\u00e1 tr\u1ecb nh\u1ecf nh\u1ea5t c\u1ee7a h\u00e0m s\u1ed1 G\u1ecdi x, y l\u1ea7n l\u01b0\u1ee3t l\u00e0 chi\u1ec1u r\u1ed9ng v\u00e0 chi\u1ec1u cao c\u1ee7a b\u1ec3 c\u00e1 (\u0111i\u1ec1u ki\u1ec7n x, y > 0 ). V\u1edbi gi\u1ea3 thi\u1ebft c\u1ee7a b\u00e0i to\u00e1n, th\u1ec3 t\u00edch b\u1ec3 c\u00e1 l\u00e0 V = 2x2y. T\u1ed5ng di\u1ec7n t\u00edch c\u00e1c m\u1eb7t k\u00ednh: S = 2xy + 2 \u00b7 2xy + 2x2 = 5. \u21d4 6xy + 2x2 = 5 \u21d4 y = 5 \u2212 2x2 . 6x \u20265 y . Do x, y > 0 n\u00ean x > 0 v\u00e0 5 \u2212 2x2 > 0 \u21d4 0 < x < 2 x 2x Nh\u01b0 v\u1eady V = 2x2y = 5x \u2212 2x3 \u21d2 V 5 \u2212 6x2 =. 33 \u20265 Cho V = 0 \u21d4 5 \u2212 6x2 = 0 \u21d4 x = . 6 x0 \u20265 \u20265 V 2 6 +0\u2212 \u221a 5 30 V 27 00 5 \u221a 30 \u2248 1,01 m3. V\u1eady dung t\u00edch l\u1edbn nh\u1ea5t c\u1ee7a b\u1ec3 c\u00e1 l\u00e0 max V = 27 Ch\u1ecdn \u0111\u00e1p \u00e1n A \u0104 C\u00e2u 44 (C\u00e2u 33 - M\u0110 101 - BGD&\u0110T - N\u0103m 2016 - 2017). x+m Cho h\u00e0m s\u1ed1 y = (m l\u00e0 tham s\u1ed1 th\u1ef1c) th\u1ecfa m\u00e3n min y = 3. M\u1ec7nh \u0111\u1ec1 n\u00e0o d\u01b0\u1edbi \u0111\u00e2y \u0111\u00fang? x\u22121 [2;4] A m < \u22121. B 3 < m \u2264 4. C m > 4. D 1 \u2264 m < 3. \u0253 L\u1eddi gi\u1ea3i. \u0110\u1ea1o h\u00e0m: y = \u22121 \u2212 m . (x \u2212 1)2 V\u1edbi \u22121 \u2212 m > 0 \u21d2 m < \u22121 \u21d2 min y = y(2) \u21d2 2+m = 3 \u21d2 m = 1 \u21d2 lo\u1ea1i. [2;4] 1 V\u1edbi \u22121 \u2212 m < 0 \u21d2 m > \u22121 \u21d2 min y = y(4) \u21d2 4+m = 3 \u21d2 m = 5 \u21d2 m > 4. [2;4] 3 Ch\u1ecdn \u0111\u00e1p \u00e1n C \u0104 C\u00e2u 45 (C\u00e2u 15 - M\u0110 103 - BGD&\u0110T - N\u0103m 2016 - 2017). T\u00ecm gi\u00e1 tr\u1ecb nh\u1ecf nh\u1ea5t m c\u1ee7a h\u00e0m s\u1ed1 y = x4 \u2212 x2 + 13 tr\u00ean \u0111o\u1ea1n [\u22122; 3]. A m= 51 B 49 C m = 13. D 51 . m= . m= . 4 4 2 \u0253 L\u1eddi gi\u1ea3i. \uf8ee x=0 \u221a \u21d2 min y = 51 2 C\u00f3 y = 4x3 \u2212 2x \u21d2 y = 0 \u21d4 \uf8f0 \u221a 4 t\u1ea1i x = \u00b1 2 x 2 = \u00b1 2 Ch\u1ecdn \u0111\u00e1p \u00e1n A \u0104 C\u00e2u 46 (C\u00e2u 42 - \u0110TK - BGD&\u0110T - l\u1ea7n 1 - N\u0103m 2019 - 2020). G\u1ecdi S l\u00e0 t\u1eadp h\u1ee3p t\u1ea5t c\u1ea3 c\u00e1c gi\u00e1 tr\u1ecb th\u1ef1c c\u1ee7a tham s\u1ed1 m sao cho gi\u00e1 tr\u1ecb l\u1edbn nh\u1ea5t c\u1ee7a h\u00e0m s\u1ed1 f (x) = |x3 \u2212 3x + m| tr\u00ean \u0111o\u1ea1n [0; 3] b\u1eb1ng 16. T\u1ed5ng t\u1ea5t c\u1ea3 c\u00e1c ph\u1ea7n t\u1eed c\u1ee7a S b\u1eb1ng Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t 90 S\u0110T: 0905.193.688","Ch\u01b0\u01a1ng 1. \u1ee8NG D\u1ee4NG \u0110\u1ea0O H\u00c0M \u0110\u1ec2 KH\u1ea2O S\u00c1T V\u00c0 V\u1ebc \u0110\u1ed2 TH\u1eca C\u1ee6A H\u00c0M S\u1ed0 A \u221216. B 16. C \u221212. D \u22122. \u0253 L\u1eddi gi\u1ea3i. X\u00e9t h\u00e0m s\u1ed1 g(x) = x3 \u2212 3x + m tr\u00ean R. g (x) = 3x2 \u2212 3; g (x) = 0 \u21d4 x = \u00b11. B\u1ea3ng bi\u1ebfn thi\u00ean c\u1ee7a h\u00e0m s\u1ed1 g(x) Ta x\u00e9t c\u00e1c tr\u01b0\u1eddng h\u1ee3p sau: +) m + 18 \u2264 0 \u21d4 m \u2264 \u221218. Khi \u0111\u00f3 m \u2212 2 < m < m + 18 \u2264 0 , n\u00ean M ax y = M ax {|m \u2212 2| , |m| , |m + 18|} = |m \u2212 2| = 2 \u2212 m. [0;3] [0;3] V\u1eady M ax y = 16 \u21d4 2 \u2212 m = 16 \u21d4 m = \u221214 (lo\u1ea1i). [0;3] +) m < 0 < m + 18 \u21d4 \u221218 < m < 0. Khi \u0111\u00f3 m \u2212 2 < m < 0 < m + 18 , \uf8f1M ax y = M ax {|m \u2212 2| , |m| , |m + 18|} = M ax {2 \u2212 m, \u2212m, m + 18} \uf8f4 \uf8f4 [0;3] [0;3] [0;3] \uf8f2 n\u00ean \u00ae2 \u2212 m, \u221218 < m < \u22128 = M ax {2 \u2212 m, m + 18} = \uf8f4 m + 18, 0 > m \u2265 \u22128 \uf8f4 \uf8f3 [0;3] V\u1eady M ax y = 16 \u21d4 \u00ae2 \u2212 m = 16, \u221218 < m < \u22128 .Nh\u01b0 v\u1eady \u00f1m = \u221214 [0;3] m + 18 = 16, \u22128 \u2264 m < 0 m = \u22122 +) m = 0 : M ax y = 18 = 16 (lo\u1ea1i). [0;3] +) m \u2212 2 < 0 < m < m + 18 Ta c\u00f3 M ax y = M ax {|m \u2212 2| , |m| , |m + 18|} = M ax {2 \u2212 m, m, m + 18} = m + 18, [0;3] [0;3] [0;3] Do \u0111\u00f3M ax y = 16 \u21d4 m + 18 = 16 \u21d4 m = \u22122 (th\u1ecfa m\u00e3n). [0;3] +) 0 \u2264 m \u2212 2 < m < m + 18. Ta c\u00f3 M ax y =M ax {|m \u2212 2| , |m| , |m + 18|} = M ax {m \u2212 2, m, m + 18} = m + 18. [0;3] [0;3] [0;3] Do \u0111\u00f3 M ax y = 16 \u21d4 m + 18 = 16 \u21d4 m = \u22122 (lo\u1ea1i). [0;3] Suy ra S = {\u221214 ; \u22122} . V\u1eady t\u1ed5ng c\u00e1c ph\u1ea7n t\u1eed c\u1ee7a S b\u1eb1ng \u221214 + (\u22122) = \u221216. Ch\u1ecdn \u0111\u00e1p \u00e1n A \u0104 C\u00e2u 47 (C\u00e2u 48 - \u0110TK - BGD&\u0110T - l\u1ea7n 2 - N\u0103m 2019 - 2020). x+m Cho h\u00e0m s\u1ed1 y = (m l\u00e0 tham s\u1ed1 th\u1ef1c). G\u1ecdi S l\u00e0 t\u1eadp h\u1ee3p t\u1ea5t c\u1ea3 c\u00e1c gi\u00e1 tr\u1ecb c\u1ee7a m sao cho x+1 max |f (x)| + min |f (x)| = 2. S\u1ed1 ph\u1ea7n t\u1eed c\u1ee7a S l\u00e0 [0;1] [0;1] A 6. B 2. C 1. D 4. \u0253 L\u1eddi gi\u1ea3i. 1\u2212m Ta c\u00f3 f (x) = (x + 1)2 . N\u1ebfu m = 1 th\u00ec f (x) = x + 1 = 1, \u2200x = \u22121. Khi \u0111\u00f3 max |f (x)| + min |f (x)| = 2 (th\u1ecfa m\u00e3n). x+1 [0;1] [0;1] Do \u0111\u00f3 m = 1 th\u1ecfa m\u00e3n b\u00e0i to\u00e1n. N\u1ebfu m = 1 th\u00ec h\u00e0m s\u1ed1 \u0111\u01a1n \u0111i\u1ec7u tr\u00ean [0; 1]. TH 1. \u00c5m + 1\u00e3 \u00b7 m \u2264 0 th\u00ec min |f (x)| = 0, max |f (x)| = max \u00df |m + 1| \u2122 ; |m| . 2 [0;1] [0;1] 2 Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t 91 S\u0110T: 0905.193.688","3. Gi\u00e1 tr\u1ecb l\u1edbn nh\u1ea5t v\u00e0 gi\u00e1 tr\u1ecb nh\u1ecf nh\u1ea5t c\u1ee7a h\u00e0m s\u1ed1 Do \u0111\u00f3 m+1 + m+1 \u2212m +m max |f (x)| + min |f (x)| = 2 \u21d4 0 + 2 2 =2 2 [0;1] [0;1] \uf8ee m \u2265 1 : m = 2( lo\u1ea1i) \u21d4 |3m + 1| + |m \u2212 1| = 2 \u21d4 \uf8ef 1 > m \u2265 \u22121 : m = 3( lo\u1ea1i) 4 \uf8ef 3 \uf8ef \uf8f0 m < \u22121 : m = \u22122( lo\u1ea1i) 3 \u00c5m + 1\u00e3 \u00df|m + 1| \u2122 \u00df|m + 1| \u2122 TH 2. \u00b7 m > 0 th\u00ec min |f (x)| = min ; |m| , max |f (x)| = max ; |m| . 2 [0;1] 2 [0;1] 2 Do \u0111\u00f3 max |f (x)| + min |f (x)| = 2 [0;1] [0;1] m+1 \u2212 m+1 \u2212m m+1 + m+1 \u2212m +m +m \u21d42 2 +2 2 =2 22 \u21d4 ||3m + 1| \u2212 |m \u2212 1|| + |3m + 1| + |m \u2212 1| = 2 44 \u00f1|3m + 1| \u2265 |m + 1| : 2|3m + 1| = 8 (2) \u21d4 |3m + 1| < |m + 1| : 2|m \u2212 1| = 8 (3) m = 1( th\u1ecfa) Gi\u1ea3i (2) \u21d4 m = \u22125( th\u1ecfa). 3 \u00ef m = 5( lo\u1ea1i) Gi\u1ea3i (3) \u21d4 m = \u22123( lo\u1ea1i). \u00df \u22125 \u2122 V\u1eady S = 1; . 3 Ch\u1ecdn \u0111\u00e1p \u00e1n B \u0104 C\u00e2u 48 (C\u00e2u 45 - M\u0110 103 - BGD&\u0110T - \u0110\u1ee3t 1 - N\u0103m 2019 - 2020). X\u00e9t c\u00e1c s\u1ed1 th\u1ef1c kh\u00f4ng \u00e2m x v\u00e0 y tho\u1ea3n m\u00e3n 2x + y.4x+y\u22121 \u2265 3 Gi\u00e1 tr\u1ecb nh\u1ecf nh\u1ea5t c\u1ee7a bi\u1ec3u th\u1ee9c P = x2 + y2 + 2x + 4y b\u1eb1ng A 33 B 9 C 21 D 41 . . . . 8 8 4 8 \u0253 L\u1eddi gi\u1ea3i. Ta c\u00f3 2x + y.4x+y\u22121 \u2265 3 \u21d4 (2x \u2212 3) .4\u2212x + y.4y\u22121 \u2265 0 \u21d4 2y.22y \u2265 (3 \u2212 2x) 23\u22122x(1) X\u00e9t tr\u01b0\u1eddng h\u1ee3p: 3 \u2212 2x \u2264 0 \u21d4 x \u2265 3 . 2 \uf8f13 \uf8f2x \u2265 21 (1) \u0111\u00fang v\u1edbi m\u1ecdi gi\u00e1 tr\u1ecb 2 \u21d2P = x2 + y2 + 2x + 4y \u2265 (2) 4 \uf8f3y \u2265 0 X\u00e9t tr\u01b0\u1eddng h\u1ee3p: 3 \u2212 2x > 0 \u21d4 0 \u2264 x < 3 92 S\u0110T: 0905.193.688 2 Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t","Ch\u01b0\u01a1ng 1. \u1ee8NG D\u1ee4NG \u0110\u1ea0O H\u00c0M \u0110\u1ec2 KH\u1ea2O S\u00c1T V\u00c0 V\u1ebc \u0110\u1ed2 TH\u1eca C\u1ee6A H\u00c0M S\u1ed0 X\u00e9t h\u00e0m s\u1ed1 f (t) = t.2t v\u1edbi t \u2265 0 \u21d2 f (t) = 2t + t.2t. ln 2 > 0 v\u1edbi m\u1ecdi t \u2265 0 . (1) \u21d4 f (2y) \u2265 f (3 \u2212 2x)\u21d4 2y \u2265 3 \u2212 2x \u21d4 y \u2265 3 \u2212 x 2 Khi \u0111\u00f3: P = x2+y2+2x+4y \u2265 x2 \u00c5 3 \u2212 \u00e32 = 2x2\u22125x+ 33 = \u00c5 \u2212 5 \u00e32 41 \u2265 41 (3) + x +2x+2 (3 \u2212 2x) 2x + 2 4 4 88 41 5 1 So s\u00e1nh (2) v\u00e0 (3) ta th\u1ea5y GTNN c\u1ee7a P l\u00e0 khi x = , y = . 8 44 Ch\u1ecdn \u0111\u00e1p \u00e1n D \u0104 C\u00e2u 49 (C\u00e2u 46 - M\u0110 103 - BGD&\u0110T - \u0110\u1ee3t 2 - N\u0103m 2019 - 2020). X\u00e9t c\u00e1c s\u1ed1 th\u1ef1c x, y th\u1ecfa m\u00e3n 2x2+y2+1 \u2264 (x2 + y2 \u2212 2x + 2)4x. Gi\u00e1 tr\u1ecb nh\u1ecf nh\u1ea5t c\u1ee7a bi\u1ec3u th\u1ee9c 8x + 4 P = 2x \u2212 y + 1 g\u1ea7n nh\u1ea5t v\u1edbi s\u1ed1 n\u00e0o d\u01b0\u1edbi \u0111\u00e2y? A 1. B 2. C 3. D 4. \u0253 L\u1eddi gi\u1ea3i. Ta c\u00f3 2x2+y2+1 \u2264 (x2 + y2 \u2212 2x + 2)4x \u21d4 2x2+y2\u22122x+1 \u2264 (x2 + y2 \u2212 2x + 1) + 1. \u0110\u1eb7t t = x2 + y2 \u2212 2x + 1. Ta c\u00f3 t = (x \u2212 1)2 + y2 n\u00ean t \u2265 0. \u0110i\u1ec1u ki\u1ec7n \u0111\u00e3 cho tr\u1edf th\u00e0nh 2t \u2264 t + 1 \u21d4 2t \u2212 t \u2212 1 \u2264 0, v\u1edbi t \u2265 0. (\u2217) X\u00e9t h\u00e0m s\u1ed1 f (t) = 2t \u2212 t \u2212 1 v\u1edbi t \u2265 0. Ta c\u00f3 f (t) = 2t \u00b7 ln 2 \u2212 1, f (t) = 0 \u21d4 t = t0 = log2(log2 e) \u2248 0,52. H\u00e0m s\u1ed1 f (t) c\u00f3 b\u1ea3ng bi\u1ebfn thi\u00ean tr\u00ean n\u1eeda kho\u1ea3ng [0; +\u221e) nh\u01b0 h\u00ecnh d\u01b0\u1edbi \u0111\u00e2y t0 t0 1 +\u221e f (t) \u22120+ +\u221e 0 0 f (t) f (t0) D\u1ef1a v\u00e0o b\u1ea3ng bi\u1ebfn thi\u00ean suy ra nghi\u1ec7m c\u1ee7a b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh (\u2217) l\u00e0 t \u2208 [0; 1]. T\u1eeb \u0111\u00f3 suy ra (x \u2212 1)2 + y2 \u2264 1. V\u1eady t\u1eadp h\u1ee3p c\u00e1c \u0111i\u1ec3m (x; y) th\u1ecfa m\u00e3n \u0111i\u1ec1u ki\u1ec7n \u0111\u00e3 cho l\u00e0 h\u00ecnh tr\u00f2n (S) t\u00e2m I(1; 0), b\u00e1n k\u00ednh R = 1. V\u1edbi c\u00e1c c\u1eb7p s\u1ed1 (x; y) th\u1ecfa m\u00e3n \u0111i\u1ec1u ki\u1ec7n 2x \u2212 y + 1 = 0, ta c\u00f3 P = 8x + 4 \u21d4 (2P \u2212 8)x \u2212 P y + P \u22124 = 0. 2x \u2212 y + 1 Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t 93 S\u0110T: 0905.193.688","3. Gi\u00e1 tr\u1ecb l\u1edbn nh\u1ea5t v\u00e0 gi\u00e1 tr\u1ecb nh\u1ecf nh\u1ea5t c\u1ee7a h\u00e0m s\u1ed1 G\u1ecdi \u2206 l\u00e0 \u0111\u01b0\u1eddng th\u1eb3ng c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh (2P \u2212 8)x \u2212 P y + P \u2212 4 = 0. Khi \u0111\u00f3 \u0111i\u1ec1u ki\u1ec7n \u0111\u1ec3 t\u1ed3n t\u1ea1i \u0111i\u1ec3m (x; y) l\u00e0 d(I, \u2206) \u2264 R \u21d4 |(2P \u2212 8) \u00b7 1 \u2212 P \u00b7 0 + P \u2212 4| \u22641 (2P \u2212 8)2 + (\u2212P )2 \u221a \u21d4 |3P \u2212 12| \u2264 5P 2 \u2212 32P + 64 \u21d4 9P 2 \u2212 72P + 144 \u2264 5P 2 \u2212 32P + 64 \u21d4 4P 2 \u2212 40P + 80 \u2264 0 \u221a\u221a \u21d4 5 \u2212 5 \u2264 P \u2264 5 + 5. \u221a V\u1eady min P = 5 \u2212 5 \u2248 2,76. Suy ra P g\u1ea7n v\u1edbi gi\u00e1 tr\u1ecb 3 nh\u1ea5t. Ch\u1ecdn \u0111\u00e1p \u00e1n C \u0104 C\u00e2u 50 (C\u00e2u 48 - M\u0110 104 - BGD&\u0110T - N\u0103m 2016 - 2017). Cho h\u00e0m s\u1ed1 y = f (x). \u0110\u1ed3 th\u1ecb c\u1ee7a h\u00e0m s\u1ed1 y = f (x) nh\u01b0 h\u00ecnh b\u00ean. y \u0110\u1eb7t g(x) = 2f (x) + (x + 1)2. \u22123 21 3 M\u1ec7nh \u0111\u1ec1 n\u00e0o d\u01b0\u1edbi \u0111\u00e2y \u0111\u00fang? Ox A g(1) < g(3) < g(\u22123). B g(1) < g(\u22123) < g(3). \u22122 C g(3) = g(\u22123) < g(1). D g(3) = g(\u22123) > g(1). \u22124 \u0253 L\u1eddi gi\u1ea3i. g (x) = 2f (x) + 2(x + 1). y T\u1eeb \u0111\u1ed3 th\u1ecb ta c\u00f3 g (x) = 0 c\u00f3 3 nghi\u1ec7m l\u00e0 \u22123; 1; 3 \u22123 21 3 Ox v\u00e0 c\u00f3 g(1) < g(3), g(\u22123). \u22122 1 3 \u22124 M\u1eb7t kh\u00e1c c\u0169ng t\u1eeb \u0111\u1ed3 th\u1ecb ta c\u00f3 (\u2212g (x)) dx > (\u2212g (x)) dx. \u22123 1 Suy ra g(3) < g(\u22123). V\u1eady ta c\u00f3 g(1) < g(3) < g(\u22123). Ch\u1ecdn \u0111\u00e1p \u00e1n A \u0104 C\u00e2u 51 (C\u00e2u 34 - M\u0110 104 - BGD&\u0110T - N\u0103m 2016 - 2017). M\u1ed9t v\u1eadt chuy\u1ec3n \u0111\u1ed9ng theo quy lu\u1eadt s = \u2212 1 t3 + 6t2 v\u1edbi t (gi\u00e2y) l\u00e0 kho\u1ea3ng th\u1eddi gian t\u00ednh t\u1eeb khi 3 v\u1eadt b\u1eaft \u0111\u1ea7u chuy\u1ec3n \u0111\u1ed9ng v\u00e0 s (m\u00e9t) l\u00e0 qu\u00e3ng \u0111\u01b0\u1eddng v\u1eadt di chuy\u1ec3n \u0111\u01b0\u1ee3c trong kho\u1ea3ng th\u1eddi gian \u0111\u00f3. H\u1ecfi trong kho\u1ea3ng th\u1eddi gian 9 gi\u00e2y, k\u1ec3 t\u1eeb khi b\u1eaft \u0111\u1ea7u chuy\u1ec3n \u0111\u1ed9ng, v\u1eadn t\u1ed1c l\u1edbn nh\u1ea5t c\u1ee7a v\u1eadt \u0111\u1ea1t \u0111\u01b0\u1ee3c b\u1eb1ng bao nhi\u00eau? A 144 m\/s. B 36 m\/s. C 243 m\/s. D 27 m\/s. \u0253 L\u1eddi gi\u1ea3i. V\u1eadn t\u1ed1c c\u1ee7a v\u1eadt \u0111\u01b0\u1ee3c t\u00ednh b\u1edfi: v(t) = \u2212t2 + 12t. Ta c\u00f3 v (t) = \u22122t + 12. B\u1ea3ng bi\u1ebfn thi\u00ean: t0 6 9 v +0\u2212 v 36 0 27 Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t 94 S\u0110T: 0905.193.688","Ch\u01b0\u01a1ng 1. \u1ee8NG D\u1ee4NG \u0110\u1ea0O H\u00c0M \u0110\u1ec2 KH\u1ea2O S\u00c1T V\u00c0 V\u1ebc \u0110\u1ed2 TH\u1eca C\u1ee6A H\u00c0M S\u1ed0 D\u1ef1a v\u00e0o b\u1ea3ng bi\u1ebfn thi\u00ean ta c\u00f3 v\u1eadn t\u1ed1c l\u1edbn nh\u1ea5t c\u1ee7a v\u1eadt \u0111\u1ea1t \u0111\u01b0\u1ee3c b\u1eb1ng 36 m\/s. Ch\u1ecdn \u0111\u00e1p \u00e1n B Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t 95 S\u0110T: 0905.193.688","4. \u0110\u01b0\u1eddng ti\u1ec7m c\u1eadn B\u00c0I 4. \u0110\u01af\u1edcNG TI\u1ec6M C\u1eacN \u0104 C\u00e2u 1 (C\u00e2u 1 - \u0110TN - BGD&\u0110T - N\u0103m 2016 - 2017). 2x + 1 \u0110\u01b0\u1eddng th\u1eb3ng n\u00e0o d\u01b0\u1edbi \u0111\u00e2y l\u00e0 ti\u1ec7m c\u1eadn \u0111\u1ee9ng c\u1ee7a \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 y = x+1 ? A x = 1. B y = \u22121. C y = 2. D x = \u22121. \u0253 L\u1eddi gi\u1ea3i. Ta c\u00f3 lim y = lim 2x + 1 = \u2212\u221e v\u00e0 lim y = lim 2x + 1 = +\u221e. x\u2192\u22121+ x\u2192\u22121+ x + 1 x\u2192\u22121\u2212 x\u2192\u22121\u2212 x + 1 Suy ra \u0111\u01b0\u1eddng th\u1eb3ng x = \u22121 l\u00e0 \u0111\u01b0\u1eddng ti\u1ec7m c\u1eadn \u0111\u1ee9ng c\u1ee7a \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 y = 2x + 1 . x+1 Ch\u1ecdn \u0111\u00e1p \u00e1n D \u0104 C\u00e2u 2 (C\u00e2u 11 - M\u0110 101 - BGD&\u0110T - N\u0103m 2017 - 2018). \u0110\u01b0\u1eddng cong trong h\u00ecnh v\u1ebd b\u00ean l\u00e0 c\u1ee7a h\u00e0m s\u1ed1 n\u00e0o d\u01b0\u1edbi \u0111\u00e2y? y A y = x4 \u2212 3x2 \u2212 1. B y = x3 \u2212 3x2 \u2212 1. O C y = \u2212x3 + 3x2 \u2212 1. D y = \u2212x4 + 3x2 \u2212 1. x \u0253 L\u1eddi gi\u1ea3i. V\u00ec \u0111\u1ed3 th\u1ecb c\u00f3 d\u1ea1ng h\u00ecnh ch\u1eef M n\u00ean kh\u00f4ng th\u1ec3 l\u00e0 \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 b\u1eadc ba. V\u00ec lim y = \u2212\u221e n\u00ean ch\u1ecdn y = \u2212x4 + 3x2 \u2212 1. x\u2192\u00b1\u221e Ch\u1ecdn \u0111\u00e1p \u00e1n D \u0104 C\u00e2u 3 (C\u00e2u 23 - M\u0110 104 - BGD&\u0110T - N\u0103m 2018 - 2019). Cho h\u00e0m s\u1ed1 y = f (x) c\u00f3 b\u1ea3ng bi\u1ebfn thi\u00ean nh\u01b0 sau: x \u2212\u221e 0 3 +\u221e 3 f (x) \u2212 \u22120+ 0 +\u221e f (x) \u22124 \u22123 T\u1ed5ng s\u1ed1 ti\u1ec7m c\u1eadn \u0111\u1ee9ng v\u00e0 ti\u1ec7m c\u1eadn ngang c\u1ee7a \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 \u0111\u00e3 cho l\u00e0 A 2. B 1. C 3. D 4. \u0253 L\u1eddi gi\u1ea3i. Ta c\u00f3 lim f (x) = 3 v\u00e0 lim f (x) = 0 n\u00ean \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 c\u00f3 2 ti\u1ec7m c\u1eadn ngang l\u00e0 c\u00e1c \u0111\u01b0\u1eddng th\u1eb3ng x\u2192+ \u221e x\u2192\u2212 \u221e c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh y = 3 v\u00e0 y = 0. Ta l\u1ea1i c\u00f3 lim f (x) = + \u221e n\u00ean h\u00e0m s\u1ed1 c\u00f3 1 ti\u1ec7m c\u1eadn \u0111\u1ee9ng l\u00e0 \u0111\u01b0\u1eddng th\u1eb3ng c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh x = 0. x\u21920+ V\u1eady h\u00e0m s\u1ed1 c\u00f3 ba ti\u1ec7m c\u1eadn. Ch\u1ecdn \u0111\u00e1p \u00e1n C \u0104 C\u00e2u 4 (C\u00e2u 15 - \u0110TK - BGD&\u0110T - l\u1ea7n 2 - N\u0103m 2019 - 2020). Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t 96 S\u0110T: 0905.193.688","Ch\u01b0\u01a1ng 1. \u1ee8NG D\u1ee4NG \u0110\u1ea0O H\u00c0M \u0110\u1ec2 KH\u1ea2O S\u00c1T V\u00c0 V\u1ebc \u0110\u1ed2 TH\u1eca C\u1ee6A H\u00c0M S\u1ed0 Ti\u1ec7m c\u1eadn ngang c\u1ee7a \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 y = x\u22121 l\u00e0 x+1 A y = \u22122. B y = 1. C x = \u22121. D x = 2. \u0253 L\u1eddi gi\u1ea3i. Ta c\u00f3 lim y = lim y = 1. x\u2192+\u221e x\u2192\u2212\u221e Do \u0111\u00f3 y = 1 l\u00e0 ti\u1ec7m c\u1eadn ngang c\u1ee7a \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1. Ch\u1ecdn \u0111\u00e1p \u00e1n B \u0104 C\u00e2u 5 (C\u00e2u 11 - M\u0110 101 - BGD&\u0110T - \u0110\u1ee3t 1 - N\u0103m 2019 - 2020). 4x + 1 Ti\u1ec7m c\u1eadn ngang c\u1ee7a \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 y = x \u2212 1 l\u00e0 1 A y= . B y = 4. C y = 1. D y = \u22121. 4 \u0253 L\u1eddi gi\u1ea3i. Ti\u1ec7m c\u1eadn ngang c\u1ee7a \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 y = 4x + 1 a4 l\u00e0 y = = = 4. x\u22121 c1 Ch\u1ecdn \u0111\u00e1p \u00e1n B \u0104 C\u00e2u 6 (C\u00e2u 9 - M\u0110 102 - BGD&\u0110T - \u0110\u1ee3t 1 - N\u0103m 2019 - 2020). 5x + 1 Ti\u1ec7m c\u1eadn ngang c\u1ee7a \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 y = x \u2212 1 l\u00e0 1 A y = 1. B y= . C y = \u22121. D y = 5. 5 \u0253 L\u1eddi gi\u1ea3i. T\u1eadp x\u00e1c \u0111\u1ecbnh D = R \\\\ {1}. Ta c\u00f3 lim y = lim y = 5. Suy ra \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 c\u00f3 ti\u1ec7m c\u1eadn ngang y = 5. x\u2192+\u221e x\u2192\u2212\u221e Ch\u1ecdn \u0111\u00e1p \u00e1n D \u0104 C\u00e2u 7 (C\u00e2u 18 - M\u0110 103 - BGD&\u0110T - \u0110\u1ee3t 1 - N\u0103m 2019 - 2020). 2x + 1 Ti\u1ec7m c\u1eadn ngang c\u1ee7a \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 y = x \u2212 1 l\u00e0: 1 A y= . B y = \u22121. C y = 1. D y = 2. 2 \u0253 L\u1eddi gi\u1ea3i. Ta c\u00f3: 2x + 1 2 2x + 1 2 lim x\u22121 = = 2; lim x\u22121 = = 2. 1 x\u2192+\u221e 1 x\u2192\u2212\u221e 2x + 1 V\u1eady y = 2 l\u00e0 \u0111\u01b0\u1eddng ti\u1ec7m c\u1eadn ngang c\u1ee7a \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 y = x \u2212 1 . Ch\u1ecdn \u0111\u00e1p \u00e1n D \u0104 C\u00e2u 8 (C\u00e2u 6 - M\u0110 104 - BGD&\u0110T - \u0110\u1ee3t 1 - N\u0103m 2019 - 2020). 3x + 1 Ti\u1ec7m c\u1eadn ngang c\u1ee7a \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 y = x \u2212 1 l\u00e0 1 A y= . B y = 3. C y = \u22121. D y = 1. 3 \u0253 L\u1eddi gi\u1ea3i. Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t 97 S\u0110T: 0905.193.688"]
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