题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085031-17865.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085031-21943.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085031-70752.png)
(1)当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085031-88195.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085031-67718.png)
(2)若
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085032-98090.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085032-41104.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085031-21943.png)
(3)在(2)的条件下,设由
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085032-98090.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085032-46546.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085031-21943.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085032-96188.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085032-44943.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085033-20442.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085033-85784.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085033-60770.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085033-34802.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085034-51895.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085034-31138.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085034-57244.png)
解析
试题分析:(1)当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085031-88195.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085034-49209.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085033-60770.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085034-41501.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085034-90658.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085034-28835.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085035-60735.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085032-98090.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085032-41104.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085031-21943.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085032-98090.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085035-79010.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085035-78871.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085033-20442.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085035-27311.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085035-47825.png)
试题解析:(1)当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085031-88195.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085036-26303.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085036-26870.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085033-60770.png)
(2)因为
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085036-25186.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085036-83406.png)
令
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085036-23465.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085032-41104.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085037-33051.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085034-90658.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085037-95349.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085037-84218.png)
此时
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085037-21247.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085038-63067.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085034-28835.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085034-51895.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085038-82309.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085038-52352.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085038-99614.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085038-78497.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085032-41104.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085037-21247.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085035-60735.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085039-87296.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085039-20057.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085038-52352.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085039-64281.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085038-78497.png)
此时
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085032-41104.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085037-21247.png)
综上所述,使函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085037-21247.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085032-41104.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085033-34802.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085034-51895.png)
(3)由(2)知当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085034-51895.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085039-48066.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085038-52352.png)
因此
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085037-33051.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085037-21247.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085035-79010.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085035-78871.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085040-44859.png)
令
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085040-16177.png)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085040-69204.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085040-92104.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085040-55386.png)
所以当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085041-10705.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085041-82763.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085041-74221.png)
又直线
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085034-57244.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085041-61441.png)
所以曲线
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085034-31138.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085034-57244.png)
核心考点
试题【已知函数,( 为常数,为自然对数的底).(1)当时,求;(2)若在时取得极小值,试确定的取值范围;(3)在(2)的条件下,设由的极大值构成的函数为,将换元为,试】;主要考察你对函数的单调性与导数等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085009-61623.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085010-78744.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085010-87170.png)
(1)若
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085010-36432.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085011-86137.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085011-38820.png)
(2)若
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085011-66324.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085011-86137.png)
(3)若
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085011-63963.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085011-86137.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085012-43275.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085012-85878.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018084948-18082.png)
(1)当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018084948-41202.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018084949-49995.png)
(2)若函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018084949-49995.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018084949-20971.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018084949-82313.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018084949-18870.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018084949-54937.png)
(3)当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018084949-80409.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018084950-47342.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018084938-48825.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018084938-73497.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018084939-53092.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018084939-48022.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018084939-98073.png)
③
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018084939-13990.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018084940-13232.png)
A.①④ | B.②④ | C.①③ | D.②③ |
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018084929-43232.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018084930-87881.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018084930-78875.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018084930-50557.png)
A.![]() ![]() ![]() ![]() |
B.![]() ![]() ![]() ![]() |
C.![]() ![]() ![]() ![]() |
D.![]() ![]() ![]() ![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018084923-68026.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018084924-62975.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018084924-63517.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018084924-28403.png)
A.(0,1) | B.(-∞,0) | C.![]() | D.(-∞,1) |
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