已知．(1)   当a =" –" 1时，求的单调区间；(2)   对一切，恒成立，求实数a的取值范围；(3)   证明：对一切，都有成立．

题型：不详难度：来源：

已知．
(1)   当a =" –" 1时，求的单调区间；
(2)   对一切，恒成立，求实数a的取值范围；
(3)   证明：对一切，都有成立．

答案

19．(1) 时，，
由，得，∴的单调增区间为
同理可得减区间为··································································· 4分
(2) 即对恒成立
也即对恒成立
令，则

由
∴在（0，1）递减，（1，+）递增
∴
∴······················································································· 8分
(3) 即证对成立
由(1)知，的最小值为
令，则
由得0 < x < 1
∴在（0，1）递增，（1，+）递减
∴
∵
∴
结论得证····················································································· 12分

解析

略