【题文】已知函数若则( )A.B.C.D.与的大小不能确定
题型:难度:来源:
【题文】已知函数
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327101349-45385.png)
若
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327101349-71569.png)
则( )
答案
【答案】B
解析
【解析】本题考查二次函数的对称性和单调性及分析问题解决问题的能力.
函数
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327101351-37969.png)
图像是开口向上,对称轴为
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327101351-10119.png)
的抛物线;因为
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327101351-42654.png)
则
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327101352-22791.png)
又
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327101352-84995.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327101352-49447.png)
;当
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327101352-13662.png)
时,因为函数
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327101351-37969.png)
在
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327101353-19835.png)
上是增函数,所以
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327101353-11112.png)
若
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327101353-11696.png)
则
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327101353-47792.png)
由
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327101354-11625.png)
知
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327101354-64901.png)
,所以
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327101354-61083.png)
综上:
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327101354-94147.png)
故选B
举一反三
【题文】已知函数
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327101339-16340.png)
若
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327101340-10646.png)
则( )
【题文】已知函数
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327101331-55427.png)
若
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327101332-94581.png)
则 ( )
【题文】已知函数
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327101322-77850.png)
若
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327101322-48049.png)
则 ( )
【题文】函数
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327101317-55672.gif)
在区间(
【题文】 (本小题满分12分)
已知函数
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327101310-83466.gif)
和
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327101310-50564.gif)
,若对任意的
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327101310-10956.gif)
,恒有
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327101310-39193.gif)
(1) 证明:
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327101311-68680.gif)
且
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327101311-87320.gif)
(2) 证明:当
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327101311-83785.gif)
时,
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327101312-73580.gif)
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