题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017124225-65750.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017124226-18581.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017124226-86463.png)
⑴求函数
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017124226-97371.png)
⑵若对于区间
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017124226-14919.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017124227-67440.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017124227-55318.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017124227-10976.png)
⑶若过点
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017124227-49537.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017124227-82011.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017124228-56540.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017124228-87852.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017124228-95623.png)
解析
试题分析:(1)利用切点处的切线的斜率就是切点处的导数可列关于
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017124228-41271.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017124228-41271.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017124228-41271.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017124226-97371.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017124226-14919.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017124227-67440.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017124227-55318.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017124229-81462.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017124229-61648.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017124229-15302.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017124229-81060.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017124230-74291.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017124230-80806.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017124230-74291.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017124227-82011.png)
试题解析:⑴
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017124230-58988.png)
根据题意,得
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017124230-48972.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017124230-63264.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017124231-33169.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017124228-87852.png)
⑵令
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017124231-21615.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017124231-71225.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017124231-99571.png)
![]() | ![]() | ![]() | ![]() | ![]() | 1 | ![]() | 2 |
![]() | | + | | ![]() | | + | |
![]() | ![]() | 增 | 极大值 | 减 | 极小值 | 增 | 2 |
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017124235-22838.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017124235-52290.png)
所以当
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017124235-50826.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017124236-23814.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017124236-91827.png)
则对于区间
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017124226-14919.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017124227-67440.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017124236-32838.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017124236-70354.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017124236-79680.png)
⑶因为点
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017124227-49537.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017124227-82011.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017124237-28461.png)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017124237-11626.png)
因为
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017124237-61143.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017124237-80109.png)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017124237-80109.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017124238-16928.png)
即
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017124238-42203.png)
因为过点
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017124227-49537.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017124227-82011.png)
所以方程
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017124238-42203.png)
所以函数
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017124238-54401.png)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017124238-87734.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017124238-91192.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017124239-93373.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017124239-50998.png)
![]() | ![]() | 0 | ![]() | 2 | ![]() |
![]() | + | | ![]() | | + |
![]() | 增 | 极大值 | 减 | 极小值 | 增 |
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017124240-54610.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017124241-23270.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017124228-95623.png)
核心考点
试题【已知函数在点处的切线方程为.⑴求函数的解析式;⑵若对于区间上任意两个自变量的值都有,求实数的最小值;⑶若过点可作曲线的三条切线,求实数的取值范围.】;主要考察你对导数的意义等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017124221-29701.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017124221-78705.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017124222-23752.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017124203-78474.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017124203-15717.png)
(1)当
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017124203-28949.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017124203-11339.png)
(2)当
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017124204-76535.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017124203-11339.png)
(3)设
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017124204-34991.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017124203-11339.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017124146-11163.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017124147-76375.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017124147-14958.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017124147-65387.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017124148-26320.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017124148-42317.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017124134-11371.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017124135-21735.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017124135-62897.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017124135-21498.png)
(1)求a和b的值; (2)证明:
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017124136-95028.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017124118-56143.png)
(Ⅰ)当
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017124118-96643.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017124118-48436.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017124118-39639.png)
(Ⅱ)求
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017124119-87061.png)
(Ⅲ)若函数
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017124119-87061.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017124119-43198.png)
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