题目
题型:不详难度:来源:
(1)当a=0时,f(x)≥g(x)在(1,+∞),上恒成立,求实数m的取值范围;
(2)当m=2时,若函数h(x)=f(x)-g(x)在[1,3]上恰有两个不同的零点,求实数a的取值范围.
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025134-64002.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025135-54179.png)
解析
试题分析:(1) 可将问题转化为
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025135-55152.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025135-27906.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025135-31925.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025136-46476.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025136-87857.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025136-47692.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025136-65159.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025136-65631.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025136-65159.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025137-54647.png)
试题解析:
解:(1)由
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025137-54612.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025137-74087.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025137-39400.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025135-55152.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025135-27906.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025135-31925.png)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025137-74087.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025138-47176.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025136-46476.png)
求得
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025138-92633.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025138-98088.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025138-58644.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025138-11372.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025139-56026.png)
故
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025139-16437.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025139-62105.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025139-26822.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025139-54302.png)
所以,实数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025140-79950.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025134-64002.png)
(2)函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025140-60225.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025136-47692.png)
等价于方程
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025136-87857.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025136-47692.png)
令
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025136-65159.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025140-22102.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025140-31583.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025141-64849.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025141-84420.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025141-27108.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025141-28852.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025141-38599.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025142-72260.png)
函数.故
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025142-46758.png)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025142-60525.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025142-18736.png)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025142-34615.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025143-98217.png)
故a的取值范围是
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025135-54179.png)
核心考点
试题【设函数f(x)=x2-mlnx,g(x)=x2-x+a.(1)当a=0时,f(x)≥g(x)在(1,+∞),上恒成立,求实数m的取值范围;(2)当m=2时,若函】;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/20191018/20191018025124-67091.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025124-28960.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025125-90977.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025125-73398.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025125-45903.png)
(1) 求
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025125-67871.png)
(2)求
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025125-89455.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025125-27401.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025111-25615.png)
(1)求
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025111-50799.png)
(2)设
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025111-63915.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025111-11532.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025111-77895.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025111-22800.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025056-17035.png)
(1)当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025056-20112.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025056-68184.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025057-65885.png)
(2)当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025057-74673.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025057-62040.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025057-89250.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025057-62962.png)
(3)若对任意
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025058-58357.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025058-14506.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025057-62962.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025050-61792.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025050-24722.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025050-46032.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025051-38257.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025051-78751.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025051-13756.png)
A.![]() ![]() | B.![]() ![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025032-19649.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025032-33407.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025032-14649.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025032-71801.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025033-96323.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025033-38304.png)
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