题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018093551-29645.png)
(1)若
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018093551-87939.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018093551-48782.png)
(2)若函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018093552-26429.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018093552-78368.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018093552-14473.png)
(3)过坐标原点
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018093552-45726.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018093553-49042.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018093553-39800.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018093553-90242.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018093553-37652.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018093554-79395.png)
解析
试题分析:(1)利用导数求函数单调性,有四个步骤.一是求出定义域:
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018093554-67826.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018093554-13805.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018093554-49630.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018093553-90242.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018093553-37652.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018093552-26429.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018093552-78368.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018093554-59838.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018093555-21276.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018093555-51708.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018093555-21276.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018093555-21656.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018093555-91698.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018093556-76294.png)
试题解析:解: (1)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018093551-87939.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018093556-29576.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018093556-68371.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018093556-44621.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018093556-63780.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018093553-90242.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018093553-37652.png)
(2)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018093557-21772.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018093557-17036.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018093557-78042.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018093557-50655.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018093555-21276.png)
即
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018093558-64893.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018093555-21276.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018093558-76164.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018093555-21276.png)
令
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018093558-70300.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018093558-52833.png)
易知
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018093558-24946.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018093557-78042.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018093559-86730.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018093559-31201.png)
(3)设切点为
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018093555-91698.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018093559-29420.png)
切线的斜率
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018093559-32456.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018093600-70243.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018093600-59220.png)
存在性:
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018093600-22699.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018093556-76294.png)
所以,
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018093600-22699.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018093556-76294.png)
再证唯一性:设
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018093600-97896.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018093600-38616.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018093601-80526.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018093601-11701.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018093601-78247.png)
所以方程
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018093556-76294.png)
综上,切点的横坐标为
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018093553-39800.png)
核心考点
试题【设函数.(1)若,求函数的单调区间;(2)若函数在区间上是减函数,求实数的取值范围;(3)过坐标原点作曲线的切线,证明:切点的横坐标为.】;主要考察你对函数的单调性与导数等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018093532-91892.png)
(1)若
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018093532-55807.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018093532-12187.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018093532-48090.png)
(2)求函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018093532-55807.png)
(3)若
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018093532-55807.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018093532-21988.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018093533-33273.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018093519-76145.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018093519-61743.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018093519-18817.png)
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018093508-92446.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018093508-29041.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018093508-90175.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018093508-26491.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018093509-14819.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018093509-95927.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018093458-22744.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018093458-26809.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018093459-91490.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018093459-88822.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018093459-45699.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018093459-36137.jpg)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018093446-78230.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018093446-48924.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018093446-39296.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018093447-84314.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018093447-51622.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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