(12分)已知函数 (1)讨论函数的单调性; (2)设函数在区间内为减函

(12分)已知函数

(1)讨论函数的单调性;

(2)设函数在区间内为减函数,求a的取值范围。

答案

解:(1),令,则

,即时,,函数在区间上是增函数;

-------------4分

,即时,方程的两根分别为:

时, ,函数在区间上是减函数;

时,,函数在区间上是增函数。-------------8分

(2)由(1)可知函数在区间内是减函数满足:

解得。-------------12分

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