题目内容
已知函数,
的最大值为3,
的图像的相邻两对称轴间的距离为2,在
轴上的截距为2.
(1)求函数
的解析式;
(2)求
的单调递增区间.
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240515017521318.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824051501768421.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824051501783336.png)
(1)求函数
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824051501768421.png)
(2)求
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824051501768421.png)
(1)
(2)![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824051501846767.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824051501830773.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824051501846767.png)
(1)![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240515018771130.png)
依题意![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824051501893808.png)
又
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824051501939755.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240515019551048.png)
令x=0,得![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240515019711055.png)
所以函数
的解析式为![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824051501830773.png)
(还有其它的正确形式,如:
等)
(2)当
,
时
单调递增
即
,![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824051502064413.png)
∴
的增区间是![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824051501846767.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240515018771130.png)
依题意
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824051501893808.png)
又
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824051501908612.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824051501939755.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240515019551048.png)
令x=0,得
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240515019711055.png)
所以函数
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824051501986549.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824051501830773.png)
(还有其它的正确形式,如:
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240515020331312.png)
(2)当
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824051502049844.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824051502064413.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824051502080450.png)
即
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824051502095647.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824051502064413.png)
∴
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824051502080450.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824051501846767.png)
![](http://thumb.zyjl.cn/images/loading.gif)
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