1 www.tuhoc.edu.vn htttp://tuhoc.edu.vn/blog 1 0 0 x D : x f(x) (x ) M M D : f M = max f(x) x D 0 0 f(x) m m x D : x D : f(x ) m = min f(x) x D 2 i f(x i Tính f(x i ), f(a) và f(b). i ), f(a), f(b)}, Min f(x) = Min {f(x i ), f(a), f(b)} [a ; b] [a ; b] VD1 3 = HD – Ta có: 2 x 1 f (x) 3x 3 0 x 1 – Tính: f(0) = 5; f(2) = 7; f(1) = 3 [0 ; 2] [0 ; 2] 2 www.tuhoc.edu.vn htttp://tuhoc.edu.vn/blog VD2 = HD 3x 1 y x 3 – Ta có: x [0 ; 2] 2 8 y 0, (x 3) x y y 0 2 – 1 3 5 Max f(x) = 1 3 [0 ; 2] [0 ; 2] TOPPER. Chú ý – Max f(x) = max {f(a), f(b)} – Min f(x) = min{f(a), f(b)} [a ; b] [a ; b] 3 www.tuhoc.edu.vn htttp://tuhoc.edu.vn/blog 1 (a) f(x) = x 3 – 3x 2 (b) f(x) = x 4 – 3x 2 (c) 2 x f(x) 1 x 2 y 5 4x 3 ; . 2 4 (a) (b) 3x 1 y x 3 2 y (x 6) x 4 (c) 2 y x 5x 6 4 www.tuhoc.edu.vn htttp://tuhoc.edu.vn/blog i (a ; b) (i = 1, 2, … n) mà f(x i ) = 0. VD3 3 = HD – Ta có 2 x 1 y 3x 3, y 0 x 1 ( (0 ; 2)) x y y 0 1 2 0 – + 3 5 1 y x x 1 6 2 2 f(x) x x 5 www.tuhoc.edu.vn htttp://tuhoc.edu.vn/blog TOPPER. Chú ý GTCT a b f(a) f(b) GTCT x y a b f(a) f(b) GTCT x y O f(b) là GTLN trên [a ; b] f(a) là GTNN trên [a ; b] – – GTCT 6 www.tuhoc.edu.vn htttp://tuhoc.edu.vn/blog VD4: = HD – Ta có: , 2 2 x 1 y . x x 1 2 2 2 x 1 y (x x 1) y 0 x 1 x y y 1 1 – 0 0 – + + 2 3 2 2 3 VD5: = HD – Ta có: D 2 y x 3x 4. D ( ; 4] [1; ). 2 2x 3 3 y , y 0 x 2 2 x 3x 4 x y y 4 1 – 3 2 + – 0 0 D D D 1 1 7 www.tuhoc.edu.vn htttp://tuhoc.edu.vn/blog VD6: = HD – Ta có: min y = max y = 1. 3 3 y sin x cos x. y (sin x cos x)(1 sin x cos x) |t| 2. 3 3t t y 2 2 ; 2 8 www.tuhoc.edu.vn htttp://tuhoc.edu.vn/blog 7 2 y x 4 x . 8 (a) (b) 2 1 y sin x cos x , 2 2 y sin x cos x 1. (a) (b) (c) (d) 2 y 3 2x x 1 y x x 1 1 y x 5 (x 0) x x x 4 y e . e 1 9 www.tuhoc.edu.vn htttp://tuhoc.edu.vn/blog 1 (a) Trên [–4 ; 4] : max f(x) = 40, min f(x) = –41 Trên [0 ; 5] : max f(x) = 40, min f(x) = 8 (b) Trên [0 ; 3] : max f(x) = 56, min f(x) = Trên [2 ; 5] : max f(x) = 552, min f(x) = 6 (c) Trên [2 ; 4] : max f(x) = , min f(x) = 0 Trên [–3 ; –2] : max f(x) = , min f(x) = 1 4 2 3 4 3 5 4 2 Max f(x) = 3, min f(x) = 1 3 Max f(x) = , min f(x) = . 2 4 (a) Max f(x) = , min f(x) = –5 (b) Max f(x) = , min f(x) = – 12 (c) Max f(x) = , min f(x) = 0 1 3 3 13 7 2 5 Max f(x) = 21 . 4 6 Min f(x) = 3 7 Max f(x) = , min f(x) = –2 2 2 8 2 + t + (*). Min y = , max y = 2 1 y cos x cos x 2 1 2 3 2 3 . 4 25 . 8 (a) Min y = 0, max y = 2 (d) Min y = 3 (0; ).