题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132104-61747.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132104-34512.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132104-58630.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132104-73196.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132105-38285.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132104-73196.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132105-43393.png)
(Ⅰ)求直线
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132104-58630.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132105-49601.png)
(Ⅱ)若
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132105-39600.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132106-91217.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132105-38285.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132106-27005.png)
(Ⅲ)当
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132106-89931.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132106-66537.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132104-58630.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132107-68171.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132107-77443.png)
(Ⅱ)当
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132107-11004.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132106-27005.png)
(Ⅲ)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132106-66537.png)
解析
试题分析:(Ⅰ)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132107-73362.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132108-10451.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132104-58630.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132105-43393.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132104-73196.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132108-20011.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132104-58630.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132107-68171.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132104-58630.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132108-28544.png)
∴方程组
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132108-57030.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132109-10442.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132109-34722.png)
依题意,方程①有两个相等的实数根,
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132109-19628.png)
解之,得
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132109-40657.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132110-90955.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132110-63855.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132110-60764.png)
(Ⅱ)由(Ⅰ)可知
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132110-23452.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132111-88676.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132111-17170.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132111-24834.png)
∴当
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132111-50424.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132112-41683.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132112-73465.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132112-23620.png)
∴当
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132107-11004.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132106-27005.png)
(Ⅲ)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132112-69968.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132113-16858.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132113-63221.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132113-99569.png)
由(Ⅱ)知当
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132111-50424.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132113-98076.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132111-50424.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132114-80227.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132114-89501.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132106-66537.png)
点评:典型题,切线的斜率,等于在切点的导函数值。利用导数研究函数的极值,一般遵循“求导数、求驻点、研究导数的正负、确定极值”,利用“表解法”,清晰易懂。不等式的证明问题,往往通过构造函数,通过研究函数的最值达到目的。
核心考点
试题【已知,,直线与函数、的图象都相切,且与函数的图象的切点的横坐标为.(Ⅰ)求直线的方程及的值;(Ⅱ)若(其中是的导函数),求函数的最大值;(Ⅲ)当时,求证:.】;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/20191017/20191017132044-77226.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132044-94904.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132044-75310.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132044-77226.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132045-76001.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132045-41752.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132045-77551.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132045-53268.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132046-68865.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132046-27213.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132046-99834.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132046-28971.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132047-73360.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132047-26803.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132047-98593.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132047-56328.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132048-71050.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132048-81034.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132039-13794.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132039-87650.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132040-11202.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132034-51595.png)
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132027-38061.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132027-29601.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132021-24032.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132021-43460.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132021-81381.png)
A.1 | B.3 | C.4 | D.9 |
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