1、 1 ( ) ( 45 ) 1 f(x) 1 (1 a)x x 2 x 3 a0. (1) f(x) (2) x 0,1 f(x) x (1)f(x) ( f x) 1 a 2x 3x 2 .1 f x) 0 x1 1 4 3a 3 x2 1 4 3a 3 x1x2 f x)0. 5 f(x) ( x1) (x2 (x1 x2) . 6 (2) a0 x10.7 a x2 (1) f(x) 0,1 f(x) x 0 x 1 . 10 00) 8 ax 2 3x 2 0 x1 x2 h(x) ax 2 3x 2 10 9 8a0 x1 x2 3 a 0 x1x2 2 a 0 9 8a0 3 2a
2、 0 h 13 0a 9 8 . 14 3 6 4 100 m ABCD x m(x 9) 1 5 x 2m 60 m 10 m. 6 4 (1) x ( 2 1.4) (2) a /m 2 4 33 ax /m 2 12a 11 3 /m 2 x (1) x 100 2x 100 2 2x 1 5 x 2 0 2 x x x 4 x 6 (2) y y a 1 5 x 2 2 4 33 ax x 2 12a 11 10 4 1 5 x 2 2 x 2 a 11 1 25 x 4 4 3 x 3 12x 2 4 8 f(x) 1 25 x 4 4 3 x 3 12x 2 f x) 4 25 x
3、 3 4x 2 24x 4x 1 25 x 2 x 6 10 f x) 0 x 10 x 15 x 9 (9,10) 10 (10,15) 15 f x) 0 0 f(x) x 10 y x 10m . 14 4 f(x) ln(x 1) a(x 2 x) a R. (1) f(x) (2) x 0 f(x a (1) f(x) ( 1 f x) 1 x 1 a(2x 1) 2ax 2 ax a 1 x 1 . 1 g(x) 2ax 2 ax a 1 x ( 1 2 a 0 g(x) 1 f x) 0 f(x) ( 1 3 a 0 a 2 8a(1 a) a(9a 8) 4 a 0 a 8 9
4、 g(x f x f(x) ( 1 4 b a 8 9 0 2ax 2 ax a 1 0 x1 x2(x1 x2) x1 x2 1 2 x1 1 4 x2 1 4 . 5 g( 1) 1 0 1 x1 1 4 . x ( 1 x1) g(x) 0 f x) 0 f(x) x (x1 x2) g(x) 0 f x) 0 f(x) x (x2 g(x) 0 f x) 0 f(x) 6 c a 0 0 g( 1) 1 0 x1 1. x ( 1 x2) g(x) 0 f x) 0 f(x) x (x2 g(x) 0 f x) 0 f(x) . 7 a 0 f(x) a 8 9 f(x) a 8 9
5、f(x) . 8 (2) (1) a 8 9 f(x) (0 f(0) 0 x (0 f(x) 0 .9 8 9 a g x2 f(x) (0 f(0) 0 x (0 f(x) 0 . 10 a 1 g(0) 0 x2 0. x (0 x2) f(x) 5 f(0) 0 x (0 x2) f(x) 0 . 11 a 0 h(x) x ln(x 1) x (0 h x) 1 1 x 1 x x 1 0 h(x) (0 . 12 x (0 h(x) h(0) 0 ln(x 1) x. f(x) x a(x 2 x) ax 2 (1 a)x x 1 1 a ax 2 (1 a)x 0 f(x) 0
6、a 0,1. 14 5 ) f(x) ln x a e 2 x (a 0) (1) a 2 f(x) (2) f(x a x 0 a (1) a 2 f(x) ln x e x 1 f x) 1 x e x 2 x e x 2 2 x (0 e) f x) 0 f(x) (0 e) 3 x (e f x) 0 f(x) (e . 4 (2) ln x a e 2 x a 5 xln x a e 2 ax (0 g(x) xln x a e 2 ax 6 g x) ln x 1 a g x) 0 x e a 1 x (0 e a 1 ) e a 1(e a 1 g x) 0 g(x) g(x)
7、g(e a 1 ) (a 1)e a 1 a e 2 ae a 1 a e 2 e a 1 8 t(x) x e 2 e x 1 t x) 1 e x 1 t x) 0 x 1 6 x (0,1) 1 (1 t x) 0 t(x) a (0,1) g(x) t(a) t(0) e 2 1 e 1 e 0 12 a 1 g(x) t(a) a e 2 e a 1 t(2) a 1,2. 14 6 ) f(x) ex e x g(x) ax 2ln x a(a R e ) (1) f(x) (2) 0 e x0 x1 x2 g(x1) g(x2) f(x0) a (1) f(x) ex e x f
8、 x) x e x f x) 0 x 1. 2 x ( 1) f x) 0 f(x) x (1 f x) 0 f(x) f(x) x 1 f(1) 1 . 5 (2) (1) x (0,1) f(x) x (1 e f(x) f(0) 0 f(1) 1 f(e) 1 e 0 x (0 e f(x) (0,1. 7 a 0 g(x) 2ln x (0 e a g x) a 2 x ax 2 x a x 2 a x x (0 e 0 2 a e a 2 e . 8 x g x) g(x) x 0 2 a2 a 2 a e g x) 0 g(x) x g(x g 2 a 2 a 2ln 2 a g(e) a(e 1) 2. 7 x0 (0 e (0 e x1 x2 10 g(x1) g(x2) f(x0) a g 2 a g 2 a 2ln 2 a a m(a) 2 a 2ln 2 a a 2 e m a) a 2 a m a) 0 a 2. 12 a (2 m a) 0 m(a) a 2 e 2 m a) 0 m(a) a 2 e m(a m(2) 0 2 a 2ln 2 a a 2 e a(e 1) a 3 e 1 . 13 a 3 e 1 x0 (0 e (0 e x1 x2 g(x1) g(x2) f(x0). 14
