题目内容
已知函数
,
,(其中
),其部分图象如图所示。
(1)求
的解析式;
(2)求函数
在区间
上的最大值及相应的
值。![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232147554773645.jpg)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823214755337931.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823214755368433.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232147553831046.png)
(1)求
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823214755399447.png)
(2)求函数
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232147554151009.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823214755446538.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823214755461266.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232147554773645.jpg)
(I)
(II)当
时,
取得最大值
。
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823214755493896.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823214755524500.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823214755539442.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823214755586338.png)
正弦函数图像中最值点与相邻零点之间的横标距离是
,从而确定
,再必须代入最值点求得
确定解析式
;
==
,在区间
上用整体法:
,![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823214755805916.png)
解:(I)由题图可知,
,所以
,
…3分
又
,且
,所以
,……………5分
所以
。………6分
(II)由(I)
……………10分
所以
=
=
…8分
=
=
。……………10分
因为
所以
,
,故
,
当
时,
取得最大值![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823214755586338.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823214755602389.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823214755649308.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823214755664324.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823214755493896.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232147557111039.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823214755742596.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823214755446538.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823214755773614.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823214755805916.png)
解:(I)由题图可知,
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823214755820351.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823214755836585.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823214755867483.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823214755883367.png)
又
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232147558981001.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823214755929687.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823214755945531.png)
所以
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823214755493896.png)
(II)由(I)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823214755493896.png)
所以
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232147557111039.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823214756039973.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823214756054840.png)
=
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823214756070540.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823214755742596.png)
因为
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823214756132746.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823214755773614.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823214756163657.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823214755805916.png)
当
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823214755524500.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823214755539442.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823214755586338.png)
![](http://thumb.zyjl.cn/images/loading.gif)
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