题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204174941-72617.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204174941-77343.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204174941-55974.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204174942-36650.png)
(1)确定
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204174942-34999.png)
(2)若过点(0,2)可做曲线
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204174942-15565.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204174942-81664.png)
(3)设曲线
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204174941-77343.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204174943-57063.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204174943-10551.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204174943-32156.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204174943-13347.png)
(2)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204174944-28576.png)
(3)运用反证法来加以证明即可。
解析
试题分析:(1)根据题意,由于函数
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204174941-72617.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204174941-77343.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204174941-55974.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204174942-36650.png)
则可知f’(0)=0,得到
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204174943-13347.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204174944-73161.png)
(2)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204174944-15455.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204174944-82844.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204174944-74265.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204174945-24549.png)
所以,
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204174945-82007.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204174945-22225.png)
设
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204174945-19913.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204174946-57809.png)
(3)反证法:由题知
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204174946-51963.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204174946-43570.png)
两式作差得
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204174946-49068.png)
若
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204174946-15603.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204174947-46024.png)
得
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204174947-78254.png)
与已知矛盾
点评:主要是考查了导数的几何意义以及函数的最值问题,属于中档题。
核心考点
试题【设函数,曲线在点处的切线方程为(1)确定的值(2)若过点(0,2)可做曲线的三条不同切线,求的取值范围(3)设曲线在点处的切线都过点(0,2),证明:当时,】;主要考察你对函数的相关概念等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204174932-38995.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204174933-55190.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204174933-39037.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204174933-82446.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204174933-24900.png)
A.13 | B.2 | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204174920-68536.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204174920-55119.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204174920-77575.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204174920-50643.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204174920-16194.png)
(1)写出函数
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204174920-86347.png)
(2)当
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204174921-42678.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204174921-21349.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204174921-60409.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204174910-52155.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204174911-22882.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204174911-15300.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204174911-30933.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204174912-86880.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204174912-17123.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204174912-28929.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204174912-83554.png)
A.![]() | B.2 | C.![]() | D.2或![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204174819-83187.png)
A.3 | B.1 | C.-1 | D.-3 |
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204174808-99430.png)
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