题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025918-32895.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025918-49055.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025918-13748.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025919-33146.png)
(1)求函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025919-28325.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025919-96605.png)
(2)求函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025919-28325.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025919-82251.png)
(3)判断函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025920-22171.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025920-71593.png)
(2)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025920-65969.png)
(3)函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025920-22171.png)
解析
试题分析:(1) 应用导数的几何意义,确定切点处的导函数值,得切线斜率,建立
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025920-26759.png)
(2) 应用导数研究函数的最值,基本步骤明确,本题中由于
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025919-82251.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025921-92301.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025921-29147.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025919-28325.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025921-93081.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025921-75998.png)
得到
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025921-25985.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025922-54052.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025919-28325.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025922-80958.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025922-84316.png)
即
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025920-65969.png)
(3)由题意
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025922-65776.png)
求导得
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025922-58094.png)
由
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025923-42835.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025923-85037.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025923-66699.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025923-12677.png)
根据
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025924-15123.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025924-72680.png)
得到函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025920-22171.png)
试题解析:(1)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025924-40556.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025924-31873.png)
由题意,两函数在
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025919-33146.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025925-43990.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025925-13938.png)
(2)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025925-54769.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025925-83046.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025925-17686.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025926-77915.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025926-11371.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025926-14292.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025926-60167.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025926-23543.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025927-75886.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025921-29147.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025919-28325.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025921-93081.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025921-75998.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025921-25985.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025922-54052.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025919-28325.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025922-80958.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025927-26137.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025927-40302.png)
(3)由题意
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025922-65776.png)
求导得
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025927-68187.png)
由
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025923-42835.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025928-45284.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025926-11371.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025923-85037.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025928-33384.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025928-44186.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025923-66699.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025923-12677.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025928-61269.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025929-77436.png)
故函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025920-22171.png)
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025859-65280.png)
(1)求
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025859-86734.png)
(2)当函数自变量的取值区间与对应函数值的取值区间相同时,这样的区间称为函数的保值区间.设
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025859-88774.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025859-88569.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025859-88247.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025849-17581.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025849-12267.png)
(1)求函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025849-12895.png)
(2)设函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025850-76994.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025850-50249.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025850-32904.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025850-36635.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025841-41568.png)
(1)当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025841-70843.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025841-71433.png)
(2)若函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025841-60607.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025841-17378.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025841-11919.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025831-34140.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025817-69680.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025817-82760.png)
(1)求函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025817-94621.png)
(2)若对于任意
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025817-65924.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025817-25559.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025818-31319.png)
(3)设
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025818-37929.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025818-72412.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025818-84054.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025818-24914.png)
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