题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112033-86697.png)
(1)若函数 f(x)与 g(x)的图像在 x=x0处的切线平行,求x0的值
(2)当曲线
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112033-25133.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112033-45553.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112034-49643.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112034-30652.png)
解析
(1)因为
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112034-71075.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112034-93613.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112035-17583.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112035-90567.png)
(2)由(1)得切点横坐标为
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112035-38262.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112035-12622.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112035-97417.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112036-43732.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112036-95556.png)
然后构造函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112036-87939.png)
解:(1)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112034-71075.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112034-93613.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112035-17583.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112035-90567.png)
解得,
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112034-49643.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112036-23004.png)
(2)由(1)得切点横坐标为
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112035-38262.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112035-12622.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112035-97417.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112036-41007.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112037-58069.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112036-95556.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112037-85331.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112037-13765.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112037-49404.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112038-38564.png)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112037-85331.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112038-87245.png)
![]() | ![]() | ![]() | ![]() |
![]() | - | 0 | + |
![]() | ↘ | 极小值 | ↗ |
又
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112039-71709.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112039-85679.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112039-94651.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112039-30479.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112040-85446.png)
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112026-85065.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112026-92225.png)
(1)求函数f(x)的单调区间和极值;
(2)若对任意的
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112026-50654.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112027-17114.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112017-83934.png)
(Ⅰ)若曲线
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112017-55325.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112017-24067.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112017-60645.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112018-59738.png)
(Ⅱ)若函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112018-10012.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112018-91310.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112018-31927.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112018-59738.png)
已知函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018111957-44379.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018111957-64149.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018111957-42631.png)
(Ⅰ)讨论
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018111957-78323.png)
(Ⅱ)求函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018111957-78323.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018111957-59904.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018111957-34662.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018111942-54406.png)
(Ⅰ)求函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018111942-18537.png)
(Ⅱ)已知
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018111942-33410.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018111942-35312.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018111943-61005.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018111937-31285.png)
A.5,-15 | B.5,-4 | C.-4,-15 | D.5,-16 |
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