题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023537-14979.png)
(1)若曲线y=f(x)过点P(1,-1),求曲线y=f(x)在点P处的切线方程;
(2)求函数f(x)在区间[1,e]上的最大值;
(3)若函数f(x)有两个不同的零点x1,x2,求证:x1x2>e2.
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023537-39505.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023537-84718.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023537-88903.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023537-94921.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023537-88903.png)
③当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023538-12460.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023538-96654.png)
解析
试题分析:(1)根据题意首先由点
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023538-16533.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023538-52259.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023538-12222.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023537-39505.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023539-97866.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023539-64718.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023539-71761.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023539-40199.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023539-12923.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023540-77449.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023540-42467.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023539-71761.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023539-40199.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023539-12923.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023540-31740.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023537-94921.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023540-40918.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023538-12460.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023541-82340.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023539-40199.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023539-12923.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023541-72118.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023541-82251.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023541-83524.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023541-42650.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023542-32523.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023542-15925.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023542-21455.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023542-44260.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023543-82786.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023543-82786.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023543-99375.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023543-90199.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023543-87765.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023543-38881.png)
试题解析:(1)因为点
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023538-16533.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023538-52259.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023544-74918.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023538-12222.png)
因为
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023544-76669.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023537-39505.png)
(2)因为
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023539-97866.png)
①当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023539-64718.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023539-71761.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023539-40199.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023539-12923.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023544-33802.png)
②当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023540-77449.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023540-42467.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023539-71761.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023539-40199.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023539-12923.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023544-33802.png)
③当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023540-31740.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023537-94921.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023539-40199.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023544-77379.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023544-73324.png)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023545-40336.png)
④当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023540-40918.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023538-12460.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023541-82340.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023539-40199.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023539-12923.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023545-29639.png)
综上,①当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023537-84718.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023537-88903.png)
②当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023537-94921.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023537-88903.png)
③当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023538-12460.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023538-96654.png)
(3)不妨设
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023541-72118.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023541-82251.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023541-83524.png)
可得
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023545-75546.png)
要证明
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023542-32523.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023542-15925.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023542-21455.png)
因为
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023542-44260.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023543-82786.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023543-82786.png)
令
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023543-99375.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023543-90199.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023543-87765.png)
令
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023543-38881.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023545-38202.png)
故函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023546-84357.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023546-47308.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023546-68402.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023543-87765.png)
所以原不等式成立. 16分
核心考点
试题【 已知函数f(x)=lnx-mx(mR).(1)若曲线y=f(x)过点P(1,-1),求曲线y=f(x)在点P处的切线方程;(2)求函数f(x)在区间[1,e]】;主要考察你对常见函数的导数等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023525-99770.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023525-68280.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023525-67428.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023526-92810.png)
(1)求
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023526-50466.png)
(2)求
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023526-52459.png)
(3)若
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023526-71009.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023526-50466.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023527-57426.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023527-80661.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023513-79190.png)
(1)求曲线
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023513-31770.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023514-35721.png)
(2)若对于任意的
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023514-89287.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023514-49389.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023514-81168.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023507-77391.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023507-20220.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023507-51126.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023508-74284.png)
A.3 | B.4 | C.5 | D.6 |
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023454-68685.png)
(1)若直线
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023454-46410.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023455-22880.png)
(2)设
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023455-99226.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023455-57269.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023455-82187.png)
(3)设
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023455-38710.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023455-93825.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023455-12625.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023444-46264.png)
(1)讨论f(x)在区间(0,1)上的单调性;
(2)当a∈[3,+∞)时,曲线
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023444-30539.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023444-58713.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023444-30539.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023445-29472.png)
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