题目内容
函数![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823202500098710.png)
满足
,且方程
的两个根
满足
.
(1)求
解析式;
(2)若
,函数
在
上的最小值为
,求
的值.
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823202500098710.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823202500129520.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823202500145672.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823202500160520.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823202500176424.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823202500192632.png)
(1)求
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823202500207447.png)
(2)若
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823202500223370.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823202500238617.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823202500270513.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823202500285270.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823202500301283.png)
⑴由
知
的对称轴方程为
,
. --------2分
又
,故
的两根分别为
,
,从而
. ----------------4分
⑵设
,则
,其中
,
所以
在
上最小值为
. ----------6分
显然
在
上为减函数,所以
----------8分
所以有
.
解得
.
因为
,所以![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823202500800371.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823202500145672.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823202500207447.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823202500379323.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823202500394425.png)
又
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823202500192632.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823202500160520.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823202500457527.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823202500488768.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823202500504703.png)
⑵设
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823202500519418.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823202500535569.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823202500223370.png)
所以
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823202500582971.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823202500535569.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823202500285270.png)
显然
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823202500628469.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823202500535569.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232025006601047.png)
所以有
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823202500753940.png)
解得
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823202500769557.png)
因为
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823202500223370.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823202500800371.png)
略
![](http://thumb.zyjl.cn/images/loading.gif)
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