题目
题型:解答题难度:一般来源:不详
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819201204-92003.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819201204-49751.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819201204-24211.gif)
(1)求
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819201205-27212.gif)
(2)若存在
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819201205-21574.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819201205-73517.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819201205-30181.gif)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819201206-40814.gif)
过点A(1,0)作曲线C的切线,设切点
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819201206-23925.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819201206-40973.gif)
将
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819201206-23925.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819201206-63902.gif)
即
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819201206-98109.gif)
令
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819201207-35178.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819201207-91723.gif)
于是
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819201207-80458.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819201207-73641.gif)
当
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819201207-80458.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819201208-85898.gif)
当
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819201207-73641.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819201208-96860.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819201208-29801.gif)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819201208-28907.gif)
(Ⅱ)因为存在
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819201209-66367.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819201209-19570.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819201209-93993.gif)
所以存在
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819201209-66367.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819201209-51280.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819201209-36909.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819201210-66546.gif)
设
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819201210-59783.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819201210-21394.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819201210-87109.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819201210-39421.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819201211-47642.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819201211-79113.gif)
当
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819201211-79173.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819201211-61854.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819201212-96325.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819201212-90747.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819201212-35371.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819201212-96325.gif)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819201212-96325.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819201212-26507.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819201212-31562.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819201213-49297.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819201213-57481.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819201212-96325.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819201213-85464.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819201213-47406.gif)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819201213-82660.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819201214-77188.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819201214-27864.gif)
因此
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819201214-56301.gif)
解析
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819201202-49611.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819201202-29080.png)
A.1 | B.2 | C.-1 | D.-2 |
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819201200-71423.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819201200-44799.png)
A.![]() | B.![]() | C.直线![]() | D.原点对称 |
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819201157-37475.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819201157-79300.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819201157-21544.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819201149-20344.gif)
(1)若
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819201149-94721.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819201149-77109.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819201149-77109.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819201150-34507.gif)
(2)若
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819201150-21735.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819201150-70747.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819201146-94504.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819201146-74308.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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