试题分析:解:(1)当
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408240101351571011.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408240101351731203.png)
1分
当
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408240101351891306.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824010135220524.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408240101352351164.png)
2分
又
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408240101352351114.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824010135251899.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824010135033657.png)
上的最大值是
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824010135048364.png)
,最小值是
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824010135064384.png)
。 3分
(2)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408240101353131035.png)
当
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824010135329399.png)
时,令
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408240101353451153.png)
。
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824010135360804.png)
单调递减,在
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824010135095611.png)
单调递增 5分
当
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408240101353911205.png)
恒成立
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824010135407780.png)
为减函数 6分
当
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824010135423388.png)
时,
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408240101354381121.png)
恒成立
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824010135407780.png)
单调递减 。 7分
综上,当
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824010135079957.png)
单调递减,在
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824010135095611.png)
单调递增,当
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824010135111945.png)
单调递减 8分
(3)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824010135532671.png)
,依题意:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824010135547693.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824010135563659.png)
9分
又
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408240101355791089.png)
恒成立。
即
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824010135610640.png)
法(一)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824010135625704.png)
在
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824010135641622.png)
上恒成立 10分
令
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408240101356722226.png)
12分
当
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408240101356881010.png)
时
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408240101357031393.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824010135142575.png)
14分
法(二)由
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408240101357501576.png)
上恒成立。
设
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824010135766975.png)
10分
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824010135781969.png)
11分
当
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408240101357971039.png)
恒成立,无最值
当
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408240101358131875.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408240101358282077.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824010135844755.png)
14分
点评:主要是考查了导数在研究函数中的运用,根据导数的符号判定函数单调性,以及函数的 最值对于恒成立问题分离参数法来得到参数的范围,属于基础题。