1、2015 4 2014 7 . . 1 20 . . 1 y = f ( x ) f ( x ) ( x 1 , x 2 ) x 0 f ( x 1 ) = f ( x 2 ) x 0 x 1 + x 2 2 f ( x 0 ) f ( x 1 + x 2 2 ) . 1 . 2 x 0 x 1 + x 2 2 x 0 x 1 + x 2 2 ( x 0e 2 0 ( x 1 - 1 ) ( x 2 - 1 ) x 1 x 2 - ( x 1 + x 2 ) 0 l n x 1 x 2 - ( x 1 + x 2 ) + 1 2 . I f ( x ) = e - x ( 1 - x ) x
2、= 1 y = f ( x ) 0 x 1 1 x 2 . x 1 x 2 f ( x 1 ) = f ( x 2 ) x 1 e - x 1 = x 2 e - x 2 . l n x 1 - x 1 = l n x 2 - x 2 x 1 - x 2 l n x 1 - l n x 2 = 1 510160 312015 4 x 1 - x 2 l n x 1 - l n x 2 = 1 2 . 3 2011 21 f ( x ) = l n x - a x 2 + ( 2 - a ) x . I f ( x ) II III y = f ( x ) x A B A B x 0 f ( x
3、 0 ) 0 y = f ( x ) ( 0 , + ) f ( 1 a ) = 0 . x = 1 a y = f ( x ) . y = f ( x ) x A B A ( x 1 , 0 ) B ( x 2 , 0 ) 0 1 a x 1 + x 2 2 x 2 1 - x 2 2 + x 1 - x 2 l n x 1 - l n x 2 + 2 ( x 1 - x 2 ) x 1 + x 2 2 x 1 + x 2 + 1 l n x 1 - l n x 2 x 1 - x 2 + 2 2 x 1 + x 2( x 1 + x 2 ) 2 x 2 1 + x 2 2 + 2 + 1
4、2 - ( x 1 + x 2 ) x 1 + x 20 x 1 + x 2 0 . . . . . 5 f ( x 1 ) = f ( x 2 ) . . . 1 . 1 2 3 4 . . 5. 5 f ( x ) = l n x + x 2 . F ( x ) = 2 f ( x ) - 3 x 2 - k x k R F ( x ) m , n ( 0 m n ) 2 x 0 = m + n F ( x ) ( x 0 , F ( x 0 ) ) x . . . 1 . . J 2014( 7) 19 - 22 . 2 . . J 2012 ( 11 ) ( ): 34 - 37 . 32
