题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132824-26869.png)
(1)当
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132824-83459.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132824-74037.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132824-36657.png)
(2)对任意
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132824-77940.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132825-29043.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132825-36175.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132825-30959.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132825-38597.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132826-39849.png)
解析
试题分析:(Ⅰ)解:当
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132824-83459.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132826-98589.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132826-67730.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132826-71734.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132826-17563.png)
所以曲线
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132824-74037.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132824-36657.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132827-72427.png)
即
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132825-38597.png)
(Ⅱ)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132827-29741.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132827-25375.png)
记
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132827-22127.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132827-70456.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132828-96694.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132828-81101.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132828-30891.png)
故
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132828-57870.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132829-27090.png)
因为对任意
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132824-77940.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132825-29043.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132829-31677.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132825-36175.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132825-29043.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132829-65221.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132829-94690.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132829-66666.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132830-94637.png)
综上
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132826-39849.png)
点评:第一问利用导数的几何意义:函数在某一点处的导数值等于该点处的切线斜率,可求得切线斜率,进而得到切线方程;第二问也可用参变量分离法分离
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132825-30959.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132825-30959.png)
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132800-67129.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132800-45487.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132801-65779.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132800-45487.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132801-92161.png)
(I) 如果函数
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132801-13624.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132801-64571.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132801-92161.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132801-56391.png)
(Ⅱ)设函数
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132801-99875.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132801-80098.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132754-25018.png)
(1)若
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132755-91011.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132755-72059.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132755-46805.png)
(2)若
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132755-26578.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132755-13631.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132750-73263.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132743-51532.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132743-24423.png)
(1)若曲线
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132744-23361.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132744-89200.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132744-96873.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132744-78622.png)
(2)讨论函数
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132744-78622.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132732-59873.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132732-45885.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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