题目内容
已知函数
在
处取得极值
.
(1)求
的值;
(2)若关于的方程
在区间
上有实根,求实数的取值范围.
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823132141163639.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823132141179226.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823132141194145.gif)
(1)求
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823132141210227.gif)
(2)若关于的方程
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823132141225483.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823132141241219.gif)
(1)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823132141257490.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823132141272280.gif)
解:(1) ![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823132141459628.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823132141475316.gif)
由已知得:![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823132141600960.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823132141615319.gif)
解得:![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823132141257490.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823132141475316.gif)
(2) 设
,则
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823132141771848.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823132141475316.gif)
的单调增区间是![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823132141818665.gif)
的单调减区间是![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823132141943493.gif)
在区间
上递增![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823132142208318.gif)
要使关于的方程
在区间
上有实根,只需
,![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823132141615319.gif)
解得:![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823132141272280.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823132141615319.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823132141459628.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823132141475316.gif)
由已知得:
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823132141600960.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823132141615319.gif)
解得:
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823132141257490.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823132141475316.gif)
(2) 设
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823132141740791.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823132141771848.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823132141475316.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823132141803299.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823132141818665.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823132141849379.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823132141943493.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823132141803299.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823132141241219.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823132142208318.gif)
要使关于的方程
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823132141225483.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823132141241219.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823132142271733.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823132141615319.gif)
解得:
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823132141272280.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823132141615319.gif)
![](http://thumb.zyjl.cn/images/loading.gif)
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