题目内容
(14分)已知函数![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823151019135985.gif)
(1)设
>0为常数,若
上是增函数,求
的取值范围;
(2)设集合
若A
B恒成立,求实数
的取值范围
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823151019135985.gif)
(1)设
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823151019151201.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823151019166824.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823151019151201.gif)
(2)设集合
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408231510192911690.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823151019307135.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823151019322204.gif)
(1)![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823151019338754.gif)
(2)![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823151019354613.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823151019338754.gif)
(2)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823151019354613.gif)
解:⑴![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823151019385970.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823151019400814.gif)
是增函数,
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823151019478805.gif)
(2)![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823151019572858.gif)
=
因为
,设
,则
[
,1]
上式化为
由题意,上式在
[
,1]上恒成立.
记
,
这是一条开口向上抛物线,
则
或
或
解得:![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823151019354613.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823151019385970.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823151019400814.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823151019416898.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823151019478805.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823151019338754.gif)
(2)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823151019572858.gif)
=
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823151019588735.gif)
因为
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823151019619562.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823151019666388.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823151019681208.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823151019759226.gif)
上式化为
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823151019790599.gif)
由题意,上式在
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823151019681208.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823151019759226.gif)
记
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823151019837661.gif)
这是一条开口向上抛物线,
则
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823151019853775.gif)
或
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823151019884669.gif)
或
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823151019900612.gif)
解得:
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823151019354613.gif)
![](http://thumb.zyjl.cn/images/loading.gif)
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