题目内容
已知偶函数
满足条件:当
时,恒有
,且
时,有
,则
的大小关系是 ( )
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232237502141270.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232237502301304.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232237504801259.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823223750074447.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823223750090433.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823223750105673.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823223750136452.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823223750152569.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232237501831368.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232237502141270.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232237502301304.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232237504481277.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232237504801259.png)
B
解:∵0≤x≤1时,有f′(x)>0,∴f(x)在[0,1]上为增函数,
又∵f(x)是偶函数,∴在[-1,0]上为减函数,
由f(x+2)=f(x)得周期为2,所以f(x)在[1,2]上为减函数
又因为![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232237505111346.png)
所以可知![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232237505421867.png)
结合单调性可知选B
又∵f(x)是偶函数,∴在[-1,0]上为减函数,
由f(x+2)=f(x)得周期为2,所以f(x)在[1,2]上为减函数
又因为
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232237505111346.png)
所以可知
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232237505421867.png)
结合单调性可知选B
![](http://thumb.zyjl.cn/images/loading.gif)
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