题目内容
(本小题满分10分)
已知函数
的最小正周期为![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823171659266401.jpg)
(I) 求
的值;
(II) 求函数
的单调区间
已知函数
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408231716592502291.jpg)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823171659266401.jpg)
(I) 求
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823171659281461.jpg)
(II) 求函数
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823171659297588.jpg)
解:(Ⅰ)![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823171659328970.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823171659344710.gif)
.…………………………3分
∵
的最小正周期为
,
,∴
,则
.………………………5分
(Ⅱ)由(Ⅰ)知
.
,![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823171659531250.gif)
得
,
…………………………7分
,![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823171659531250.gif)
得
,![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823171659531250.gif)
∴函数
的单调增区间为
,
;单调减区间为![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823171659734660.gif)
.……………………………………10分
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823171659328970.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823171659344710.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823171659359765.gif)
∵
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823171659375287.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823171659406192.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823171659422257.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823171659437459.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823171659453242.gif)
(Ⅱ)由(Ⅰ)知
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823171659484831.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823171659500813.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823171659531250.gif)
得
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823171659547660.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823171659531250.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823171659593814.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823171659531250.gif)
得
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823171659625679.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823171659531250.gif)
∴函数
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823171659375287.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823171659687644.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823171659531250.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823171659734660.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823171659531250.gif)
略
![](http://thumb.zyjl.cn/images/loading.gif)
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