1、 1 1 f(x) ln x x (0 e _ f x) 1 x 1 1 x x (x0) f x)0 01 f(x) (0,1 (1 e x 1 f(x) (0 e f(1) 1. 1 2 f(x) 1 2 e x (sin x cos x) x 0 2 _ x 0 2 f x) e x cos x f f(x f 2 1 2 f(x 1 2 e 2 . 1 2 1 2 e 23 y x x x _. y 2 x x x ln 2 0 x 1 ln 2 . 1 ln 24 f(x) x 3 2cx 2 x c _ f(x) x 3 2cx 2 x f x) 3x 2 4cx 1 0 ( 4c
2、) 2 120 c 3 2 c0 x2 f x)0 f(x) ( 2) x ( 2,1) f x)0 f(x) (1 f(x) x 2 f( 2) 21 x 1 f(1) 6. 10 f(x) x 1 a e x(a R e ) (1) y f(x) (1 f(1) x a (2) f(x) (1) f(x) x 1 a e x f x) 1 a e x. y f(x) (1 f(1) x f 0 1 a e 0 a e. 5 (2)f x) 1 a e x a f x) 0 f(x) ( f(x) a 0 f x) 0 e x a x ln a x ( ln a) f x) 0 x (ln
3、a f x) 0 f(x) ( ln a) (ln a f(x) x ln a f(ln a) ln a a f(x) a 0 f(x) x ln a ln a 1 f(x) x 3 6x 2 9x abc a b c f(a) f(b) f(c) 0. f(0)f(1) 0 f(0)f(1) 0 f(0)f(3) 0 f(0)f(3) 0. _ f x) 3x 2 12x 9 3(x 1)(x 3) f x) 0 1 x 3 f x) 0 x 1 x 3 f(x) (1,3) ( 1) (3 a b c f(a) f(b) f(c) 0 f(x) f(1) 4 abc 0 f(x) f(3)
4、 abc 0. 0 abc 4. a b c a 0 b 0 c 0. x 1 x 3 f(x) f(0) 0. f(0)f(1) 0 f(0)f(3) 0. . 2 f(x) mx 3 nx 2 ( 1,2) 3x y 0 f(x) t t 1 t _ f x) 3mx 2 2nx f 3m 2n 3 f m n 2 m 1 n 3 f x) 3x 2 6x. f(x) t t 1 f x) 3x 2 6x t t 1 f t 3t 2 6t f t t 2 t t 2 1 6 2 1 3 ) f(x) ax 2 bx ln x(a 0 b R) (1) a 1 b 1 f(x) (2) x
5、 0 f(x f(1) ln a 2b (1) f(x) ax 2 bx ln x x (0 f x) 2ax 2 bx 1 x . a 1 b 1 f x) 2x 2 x 1 x x x x (x 0) f x) 0 x 1. 0 x 1 f x) 0 f(x) x 1 f x) 0 f(x) f(x) (0,1) f(x) (1 (2) f(x) x 1 x 1 f(x) f 0 2a b 1 b 1 2a. g(x) 2 4x ln x(x 0) g x) 1 4x x . g x) 0 x 1 4 . 0 x 1 4 g x) 0 g(x) x 1 4 g x) 0 g(x) g(x g 1 4 1 ln 1 4 1 ln 4 0 g(a) 0 2 4a ln a 2b ln a 0 ln a 2b.
