题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040411-36280.png)
(1)若存在
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040411-66424.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040412-97703.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040412-44388.png)
(2)求证:当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040412-44418.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040412-54393.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040412-44220.png)
解析
试题分析:本题主要考查导数的运算,利用导数研究函数的单调性、最值、不等式等基础知识,考查函数思想,考查综合分析和解决问题的能力.第一问,将已知条件转化为
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040412-24084.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040412-99597.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040412-99597.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040412-44220.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040413-18375.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040413-15345.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040413-41763.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040413-21907.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040413-27121.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040414-51330.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040413-15345.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040414-33833.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040414-38518.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040413-41763.png)
试题解析:
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040411-36280.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040414-65397.png)
(1)即存在
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040412-44418.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040414-41986.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040415-74394.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040415-22531.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040415-96629.png)
令
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040415-38395.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040416-26178.png)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040416-18513.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040416-29486.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040412-99597.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040416-24098.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040416-25955.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040417-12657.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040412-99597.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040417-21627.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040417-67776.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040412-44220.png)
(2)即
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040413-18375.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040417-38937.png)
令
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040417-78052.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040413-21907.png)
由(1)可知
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040413-27121.png)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040418-65480.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040413-15345.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040418-73326.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040418-22470.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040418-19874.png)
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040400-50292.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040401-58083.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040401-78150.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040401-65086.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040400-50292.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040401-58083.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040401-25726.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040401-48783.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040402-29502.png)
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040348-56851.png)
(1)当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040349-98039.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040349-75621.png)
(2)若当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040349-24892.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040349-97977.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040350-86888.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040337-71445.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040337-10268.jpg)
(1)求f(x)在x=3处的切线斜率;
(2)若f(x)在区间(m,m+
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040337-48316.png)
(3)若对任意k∈[-1,1],函数y=kx(x∈(0,6])的图象总在函数y=f(x)图象的上方,求c的取值范围
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040323-76984.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040323-11057.png)
(Ⅰ)求
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040323-62755.png)
(Ⅱ)若
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040324-92048.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040323-62755.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040324-16910.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040324-89058.png)
(其中
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040324-73833.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040307-54924.png)
(Ⅰ)当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040307-56124.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040307-86792.png)
(Ⅱ)设
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040307-30797.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040308-42390.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040308-75034.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040308-94939.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040308-84168.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040309-87010.png)
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