题目内容
已知函数
在
处都取得极值.
(1)求
、
的值;
(2)若对
时,
恒成立,求实数
的取值范围
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823211051319948.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823211051334526.png)
(1)求
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823211051334283.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823211051366299.png)
(2)若对
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823211051381546.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823211051397521.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823211051428249.png)
(1)
………………2分
在
处都取得极值
……………3分
即
………………4分
经检验符合 ………………5分
(2)由(1)可知,![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823211051553848.png)
………6分
由![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823211051615479.png)
0,得
的单调增区间为
,由![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823211051615479.png)
0,得
的单调减区间为
∴
=1是
的极大值点 ………8分
当
时,
=
-
-4,
=-3
+
+4
而
-
=4e-9-![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823211052005343.png)
所以
>
,即
在
上的最小值为
+4-3e, …………9分
要使对
时,
恒成立,必须
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823211051444890.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823211051459912.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823211051490558.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232110515061534.png)
即
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823211051522656.png)
经检验符合 ………………5分
(2)由(1)可知,
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823211051553848.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232110515841178.png)
由
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823211051615479.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823211051631221.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823211051646435.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823211051662492.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823211051615479.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823211051693207.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823211051646435.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823211051724786.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823211051740266.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823211051646435.png)
当
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823211051787542.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823211051802471.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823211051834264.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823211051849359.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823211051865428.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823211051834264.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823211051958303.png)
而
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823211051802471.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823211051865428.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823211052005343.png)
所以
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823211051802471.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823211051865428.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823211051646435.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823211051787542.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823211051958303.png)
要使对
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823211051787542.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823211052146530.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823211052161961.png)
略
![](http://thumb.zyjl.cn/images/loading.gif)
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