题目
题型:解答题难度:困难来源:不详
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154836-32036.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154836-34310.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154836-85149.png)
(1)当
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154836-70593.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154837-30636.png)
(2)若函数
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154837-30636.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154837-65619.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154836-34310.png)
(3)若对任意的
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154837-79412.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154837-97942.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154837-70941.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154838-22017.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154836-34310.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154837-30636.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154838-11690.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154838-20708.png)
(2)
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154836-34310.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154838-47141.png)
(3)
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154836-34310.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154838-26837.png)
解析
试题分析:(1)将
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154836-70593.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154837-30636.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154837-30636.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154837-30636.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154837-65619.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154839-59797.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154839-53124.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154837-65619.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154839-53124.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154837-65619.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154836-34310.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154836-34310.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154839-95331.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154837-97942.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154836-34310.png)
试题解析:(1)
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154836-70593.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154839-69944.png)
由
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154839-15324.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154840-64891.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154840-86394.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154840-11792.png)
故
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154837-30636.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154838-11690.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154838-20708.png)
(2)因为
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154840-30212.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154837-65619.png)
故要使
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154837-30636.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154837-65619.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154840-92052.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154841-91466.png)
即
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154840-92052.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154842-29931.png)
令
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154842-53399.png)
则
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154842-55392.png)
再令
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154842-23120.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154842-40824.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154837-65619.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154843-55434.png)
故
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154843-45156.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154843-65135.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154837-65619.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154843-40583.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154837-65619.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154843-15749.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154837-65619.png)
又
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154844-85771.png)
故要使
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154844-96203.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154844-85161.png)
若函数
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154837-30636.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154837-65619.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154836-34310.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154838-47141.png)
(3)
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154844-83714.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154844-67145.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154845-97179.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154845-85404.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154845-77853.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154845-44320.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154845-85404.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154845-12242.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154846-37651.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154839-95331.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154837-97942.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154846-87445.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154846-97573.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154846-97595.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154846-92769.png)
故
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154847-62465.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154847-83990.png)
此时,当
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154847-94562.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154847-82677.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154837-30636.png)
![]() | ![]() | ![]() | ![]() |
![]() | — | 0 | + |
![]() | ↘ | 最小值 | ↗ |
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154848-29442.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154848-41421.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154848-25729.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154849-60266.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154846-37651.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154837-79412.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154837-97942.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154837-70941.png)
使得
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154838-22017.png)
当且仅当
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154836-34310.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154849-86855.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154849-60885.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154849-25401.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154850-27439.png)
令
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154850-66635.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154850-11173.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154850-23642.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154850-51797.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154850-84887.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154851-80787.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154851-48976.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154851-70292.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154851-58641.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154851-48976.png)
所以在任取
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154852-83296.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154852-72534.png)
即②式对
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154852-83296.png)
由③解得
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154852-86292.png)
由①④ 当
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154852-86292.png)
对任意
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154837-79412.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154837-97942.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154837-70941.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154838-22017.png)
核心考点
试题【已知函数(为常数,为自然对数的底)(1)当时,求的单调区间;(2)若函数在上无零点,求的最小值;(3)若对任意的,在上存在两个不同的使得成立,求的取值范围.】;主要考察你对对数函数的定义等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154832-80227.png)
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154749-15917.png)
(1)求函数
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154749-50544.png)
(2)当
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154750-57333.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154750-80935.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154750-34596.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154750-80935.png)
(3)关于
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154750-88299.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154750-99367.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154751-80804.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154751-14223.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154746-65121.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154746-37323.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154746-62550.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154746-24037.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154747-17522.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154747-12622.png)
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154743-25705.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154743-96081.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154743-28468.png)
A.![]() ![]() ![]() |
B.![]() ![]() ![]() |
C.![]() ![]() ![]() |
D.![]() ![]() ![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154740-28441.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154740-47869.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154740-15244.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154740-83106.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190820/20190820154740-40467.png)
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