题目内容
已知函数
,对任意实数x都有
成立,若当
时,
恒成立,则b的取值范围是( )
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408240119480331218.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824011948049648.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824011948064477.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824011948080538.png)
A.![]() | B.![]() | C.![]() ![]() | D.不能确定 |
C
试题分析:由题意,对任意实数x都有
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824011948049648.png)
所以,
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824011948158401.png)
又因为,图象开口方向向下,所以,函数在[-1,1]上单调递增,
所以,要使当x∈[-1,1]时,f(x)>0恒成立,则有f(-1)=-1-2+
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824011948173350.png)
解得,
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824011948127383.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824011948111426.png)
点评:中档题,涉及二次函数问题,往往要考虑“开口方向,对称轴位置,与x轴交点情况,函数的单调区间”等。
![](http://thumb2018.1010pic.com/images/loading.gif)
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