题目内容
本小题满分12分)
已知向量![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823165639437978.png)
(1)令f(x)=
求f(x)解析式及单调递增区间.
(2)若![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823165639500309.png)
,求函数f(x)的最大值和最小值.
已知向量
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823165639437978.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408231656394681341.png)
(1)令f(x)=
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823165639484589.png)
(2)若
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823165639500309.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823165639562577.png)
(1)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823165639609474.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823165639624868.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823165639656421.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408231656396713825.png)
(2)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823165639702665.png)
(1)解:
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408231656396713825.png)
当
,
,即:
时,
单调递增,
增区间为:
,![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823165639656421.png)
(2)由
得
,![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408231656399361032.png)
当
时
当
时,![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823165640061633.png)
综合①②③得,方程至少有一个正根的充要条件是
。。。12分
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408231656396713825.png)
当
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823165639765826.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823165639780418.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408231656397961000.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823165639812451.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823165639609474.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823165639624868.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823165639656421.png)
(2)由
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823165639905708.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823165639921781.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408231656399361032.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823165639968193.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823165639999513.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823165640014843.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823165640030558.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823165640061633.png)
综合①②③得,方程至少有一个正根的充要条件是
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823165639702665.png)
![](http://thumb.zyjl.cn/images/loading.gif)
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