题目
题型:解答题难度:一般来源:不详
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819201106-14563.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819201106-57658.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819201106-24250.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819201106-33997.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819201106-71829.gif)
(I)求函数
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819201106-71037.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819201106-17069.gif)
(II)当
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819201106-70864.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819201106-61325.gif)
(III)若对任意的
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819201106-39559.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819201106-61325.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819201106-98920.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819201107-37640.gif)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819201107-12030.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819201107-56275.gif)
因为
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819201106-71829.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819201107-41775.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819201107-56275.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819201107-15971.gif)
当且仅当
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819201107-92508.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819201107-82026.gif)
(II)当
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819201106-70864.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819201107-63279.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819201107-70383.gif)
………………………………………………………..6分
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819201107-42555.gif)
![]() | ![]() | ![]() | ![]() | ![]() | ![]() |
![]() | ![]() | 0 | ![]() | 0 | ![]() |
![]() | ![]() | ![]() | ![]() | ![]() | ![]() |
所以,函数
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819201106-61325.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819201107-77097.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819201108-63943.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819201107-85377.gif)
……………………………………………………………….8分
函数
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819201106-61325.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819201109-62578.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819201108-96944.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819201109-30942.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819201108-95590.gif)
……………………………………………………………….10分
(III)由题意,
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819201109-67419.gif)
不妨设
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819201109-33615.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819201106-98920.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819201109-38012.gif)
令
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819201109-38284.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819201109-84940.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819201109-67571.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819201109-37205.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819201109-67571.gif)
即
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819201109-22581.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819201109-67571.gif)
因为
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819201110-69602.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819201110-83480.gif)
解得
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819201110-54356.gif)
故所求实数
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819201107-37640.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819201110-54356.gif)
解析
核心考点
试题【(本小题满分14分)已知函数,,,其中且.(I)求函数的导函数的最小值;(II)当时,求函数的单调区间及极值;(III)若对任意的,函数满足,求实数的取值范围.】;主要考察你对指数函数图象及性质等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819201102-31304.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819201102-20228.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819201100-81710.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819201100-30882.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819201100-36802.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819201100-18187.gif)
则实数
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819201101-44027.gif)
A.![]() | B.2 | C.![]() | D.4 |
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819201057-27198.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819201057-26112.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819201057-27198.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819201058-85847.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819201058-69878.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819201058-96657.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819201058-85847.gif)
A.有最大值63 | B.有最小值63 | C.有最大值31 | D.有最小值31 |
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819201053-12630.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819201053-24391.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819201053-85809.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819201047-73912.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819201047-72650.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819201048-60242.gif)
A.2009 | B.2010 | C.2011 | D.2012 |
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