【题文】函数在上的最大值比最小值大,则 .
【题文】函数在上的最大值比最小值大,则 .
题型:难度:来源:
答案
【答案】
![](http://img.shitiku.com.cn/uploads/allimg/20200328/20200328041033-16754.png)
解析
【解析】
试题分析:因为
![](http://img.shitiku.com.cn/uploads/allimg/20200328/20200328041033-13643.png)
,根据指数函数的性质可知
![](http://img.shitiku.com.cn/uploads/allimg/20200328/20200328041034-68019.png)
在
![](http://img.shitiku.com.cn/uploads/allimg/20200328/20200328041032-43805.png)
单调递增,所以最大值为
![](http://img.shitiku.com.cn/uploads/allimg/20200328/20200328041034-35830.png)
,最小值为
![](http://img.shitiku.com.cn/uploads/allimg/20200328/20200328041034-79726.png)
,依题意有
![](http://img.shitiku.com.cn/uploads/allimg/20200328/20200328041035-97169.png)
即
![](http://img.shitiku.com.cn/uploads/allimg/20200328/20200328041035-20599.png)
,而
![](http://img.shitiku.com.cn/uploads/allimg/20200328/20200328041033-13643.png)
,所以
![](http://img.shitiku.com.cn/uploads/allimg/20200328/20200328041035-31189.png)
.
考点:指数函数的图像与性质.
举一反三
【题文】设
![](http://img.shitiku.com.cn/uploads/allimg/20200328/20200328041017-17991.png)
,则( )
【题文】设
![](http://img.shitiku.com.cn/uploads/allimg/20200328/20200328040932-66057.png)
,则( )
【题文】若
![](http://img.shitiku.com.cn/uploads/allimg/20200328/20200328040925-40926.png)
,则
![](http://img.shitiku.com.cn/uploads/allimg/20200328/20200328040926-11053.png)
的取值范围为________________.
【题文】计算
(1)
![](http://img.shitiku.com.cn/uploads/allimg/20200328/20200328040903-96100.png)
;
(2)
![](http://img.shitiku.com.cn/uploads/allimg/20200328/20200328040904-80936.png)
.
【题文】已知
![](http://img.shitiku.com.cn/uploads/allimg/20200328/20200328040855-11510.png)
、
![](http://img.shitiku.com.cn/uploads/allimg/20200328/20200328040855-90978.png)
为正实数,且
![](http://img.shitiku.com.cn/uploads/allimg/20200328/20200328040855-83230.png)
,则
![](http://img.shitiku.com.cn/uploads/allimg/20200328/20200328040856-74257.png)
的最小值是( )
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