题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044115-90339.png)
(Ⅰ)如果函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044115-73931.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044115-71053.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044116-88658.png)
(Ⅱ)是否存在正实数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044116-88658.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044116-59663.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044116-90631.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044116-93243.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044116-88658.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044116-20928.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044117-70275.png)
(Ⅱ)存在,
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044116-88658.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044117-46738.png)
解析
试题分析:(Ⅰ)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044115-73931.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044115-71053.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044117-18394.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044117-82142.png)
(Ⅱ)零点的问题一般都求函数的单调区间结合函数的图象来解决.在本题中,直接研究
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044117-44549.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044118-53561.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044118-46082.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044118-52273.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044118-46082.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044118-27135.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044119-50653.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044118-27135.png)
为满足题意,只需
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044119-62009.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044118-46082.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044119-42183.png)
试题解析:解:(1)当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044119-26834.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044120-20915.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044115-71053.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044120-64489.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044115-73931.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044120-44999.png)
由于
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044115-73931.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044115-71053.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044120-10933.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044116-20928.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044121-94143.png)
综上,
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044116-88658.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044117-70275.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044116-20928.png)
(2)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044117-44549.png)
因
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044118-53561.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044118-46082.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044121-95338.png)
即方程
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044118-52273.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044118-46082.png)
设
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044118-27135.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044119-50653.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044121-20706.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044121-86045.png)
令
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044121-77927.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044116-88658.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044122-19059.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044122-76385.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044122-51858.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044122-80112.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044119-62009.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044123-65044.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044123-11522.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044119-62009.png)
为满足题意,只需
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044119-62009.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044118-46082.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044119-42183.png)
解得
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044123-70743.png)
核心考点
试题【已知函数.(Ⅰ)如果函数在区间上是单调函数,求的取值范围;(Ⅱ)是否存在正实数,使得函数在区间内有两个不同的零点(是自然对数的底数)?若存在,求出实数的取值范围】;主要考察你对常见函数的导数等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044106-14930.png)
(1)若
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044106-36373.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044106-30102.png)
(2)当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044106-28368.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044106-77365.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044107-72717.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044057-42000.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044057-53338.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044057-83043.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044040-56479.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044040-13243.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044040-26444.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044040-70345.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044040-72660.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044040-96382.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044040-28040.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044040-94331.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044041-12796.png)
(1)求常数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044040-26444.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044040-28040.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044040-94331.png)
(2)求证:对于函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044041-19769.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044041-29272.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044041-76801.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044041-67853.png)
(3)若存在
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044041-76801.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044041-38103.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044042-44577.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044025-41145.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044025-73669.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044026-53924.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044026-94696.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044026-90844.png)
(1)当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044026-69639.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044026-94043.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044026-52635.png)
(2)若
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044026-52635.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044026-21623.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044026-32074.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044005-18340.png)
(1)当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044005-63927.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044005-49554.png)
(2)求函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044005-49554.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044006-36579.png)
(3)试证明:
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044006-25574.png)
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