题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205040604-59875.png)
(Ⅰ) 设函数f(x)的图象与x轴交点为A, 曲线y=f(x)在A点处的切线方程是
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205040604-46930.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205040604-62729.png)
(Ⅱ) 若函数
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205040605-59870.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205040605-79160.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205040605-65650.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205040605-72751.png)
(Ⅱ)当
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205040605-23203.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205040605-79160.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205040606-71681.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205040606-19054.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205040606-68897.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205040605-79160.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205040606-62742.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205040606-19054.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205040607-75125.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205040607-76842.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205040605-79160.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205040607-71157.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205040607-38424.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205040605-79160.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205040607-82216.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205040606-71681.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205040608-79737.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205040608-17827.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205040605-79160.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205040607-82216.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205040608-79737.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205040606-71681.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205040608-92032.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205040605-79160.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205040607-71157.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205040608-80406.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205040605-79160.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205040606-19054.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205040607-75125.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205040606-62742.png)
解析
(1)根据已知条件,可知∵
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205040609-39270.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205040609-15479.png)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205040609-35726.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205040609-34324.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205040604-46930.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205040609-61251.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205040605-65650.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205040605-72751.png)
(2)对于参数a分情况讨论。判定导数的符号,确定函数的单调性即可。
解:(Ⅰ)∵
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205040609-39270.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205040609-15479.png)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205040609-35726.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205040609-34324.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205040604-46930.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205040609-61251.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205040605-65650.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205040605-72751.png)
(Ⅱ)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205040610-44421.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205040610-94360.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205040610-56920.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205040610-10716.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205040610-53995.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205040611-16796.png)
①当
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205040605-23203.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205040611-47646.png)
![]() | ![]() | 0 | ![]() |
![]() | - | 0 | + |
![]() | ![]() | 极小值 | ![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205040605-79160.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205040606-71681.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205040606-19054.png)
②当
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205040612-72375.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205040612-39417.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205040612-40010.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205040612-44057.png)
(ⅰ)当
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205040613-48472.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205040606-68897.png)
![]() | ![]() | 0 | ![]() | ![]() | ![]() |
![]() | - | 0 | + | 0 | - |
![]() | ![]() | 极小值 | ![]() | 极大值 | ![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205040605-79160.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205040606-62742.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205040606-19054.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205040613-96799.png)
(ⅱ)当
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205040613-23597.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205040607-76842.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205040610-10716.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205040613-75750.png)
故
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205040605-79160.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205040607-71157.png)
(ⅲ)当
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205040614-67956.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205040607-38424.png)
![]() | ![]() | ![]() | ![]() | 0 | ![]() |
![]() | - | 0 | + | 0 | - |
![]() | ![]() | 极小值 | ![]() | 极大值 | ![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205040605-79160.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205040607-82216.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205040606-71681.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205040608-79737.png)
综上所述,当
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205040605-23203.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205040605-79160.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205040606-71681.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205040606-19054.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205040606-68897.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205040605-79160.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205040606-62742.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205040606-19054.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205040607-75125.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205040607-76842.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205040605-79160.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205040607-71157.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205040607-38424.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205040605-79160.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205040607-82216.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205040606-71681.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205040608-79737.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205040608-17827.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205040605-79160.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205040607-82216.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205040608-79737.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205040606-71681.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205040608-92032.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205040605-79160.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205040607-71157.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205040608-80406.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205040605-79160.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205040606-19054.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205040607-75125.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205040606-62742.png)
核心考点
试题【(本题14分)已知函数, (Ⅰ) 设函数f(x)的图象与x轴交点为A, 曲线y=f(x)在A点处的切线方程是, 求的值;(Ⅱ) 若函数, 求函数的单调区间. 】;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/20200205/20200205040553-57322.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205040553-15709.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205040553-31824.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205040553-57322.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205040554-56001.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205040554-26844.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205040554-35925.jpg)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205040541-78910.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205040541-49249.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205040541-70120.png)
已知函数
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205040530-69230.png)
(1)若
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205040530-22441.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205040530-69495.png)
(2)若函数
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205040531-48474.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205040531-25381.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205040530-69495.png)
(3)当
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205040531-22012.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205040531-48474.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205040531-62793.png)
已知
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205040517-39884.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205040517-84365.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205040517-79559.png)
(1) 求
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205040517-10079.png)
(2) 判断
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205040517-10079.png)
(3)求使得
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205040518-87593.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205040518-55010.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205040504-65249.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205040504-87363.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205040504-38311.png)
A.1 | B.3 | C.0 | D.2 |
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