题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132601-87731.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132601-75649.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132601-53547.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132602-58425.png)
(1)若
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132602-20358.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132602-42618.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132602-64482.png)
(2)若
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132603-40972.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132603-34827.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132603-28561.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132603-95099.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132604-15475.png)
解析
试题分析:(Ⅰ) 依题有:
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132604-28899.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132604-75771.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132602-42618.png)
令
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132604-44087.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132605-93595.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132605-56250.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132605-54689.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132605-34639.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132605-53478.png)
因此,
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132604-44087.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132606-17188.png)
而
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132606-19797.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132606-83581.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132606-86421.png)
易知,
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132607-18987.png)
①当存在两个变号零点时,
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132607-49732.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132607-68232.png)
② 当存在一个变号零点时,
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132607-33155.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132608-44987.png)
综上,当
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132602-20358.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132602-42618.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132602-64482.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132603-95099.png)
(Ⅱ) 当
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132603-40972.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132608-52269.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132608-94324.png)
易知
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132609-32719.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132608-52269.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132608-94324.png)
若有公共切线,则
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132609-32719.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132609-27919.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132609-47872.png)
可知
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132608-94324.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132609-32719.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132604-15475.png)
而
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132608-52269.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132609-81145.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132609-38277.png)
可知
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132608-52269.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132609-32719.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132604-15475.png)
因此,存在一条公切线,切线方程为:
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132604-15475.png)
点评:函数在某区间有极值,则在区间上有变号零点,转化为导函数最大值最小值一正一负,第二问找到两函数的公共点
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132609-32719.png)
核心考点
试题【已知函数,,.(1)若在存在极值,求的取值范围; (2)若,问是否存在与曲线和都相切的直线?若存在,判断有几条?并求出公切线方程,若不存在,说明理由。】;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/20191017/20191017132556-37983.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132556-60736.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132556-57433.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132556-55968.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132552-60395.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132552-97884.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132552-10461.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132552-50269.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132553-24636.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132547-76439.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132547-41543.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132547-76439.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132547-55319.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132547-55319.png)
A.
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132548-76031.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132548-80920.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132548-73836.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132548-16432.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132512-94219.png)
(1)若
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132512-17753.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132512-39135.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132513-41132.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132513-92226.png)
(2)若对任意
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132513-58906.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132513-87704.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132513-22720.png)
(3)在(1)的条件下,设
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132514-21499.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132513-22720.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132514-11559.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132514-87535.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132514-16064.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132515-42444.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132515-98760.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132515-98760.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132515-85912.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017132507-38882.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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