题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113554-32485.png)
(1)若a=3,b=-2,求f(x)在[
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113555-86044.png)
(2)若b=2,f(x)存在单调递减区间,求a的范围.
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113555-86044.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113555-78584.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113555-86044.png)
(2) a的范围(-1,0)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113555-55531.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113555-59624.png)
解析
(1)由于
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113556-72447.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113556-83666.png)
(2)因为f(x)存在递减区间,
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113556-10443.png)
解:(1)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113556-53392.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113556-16120.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113556-16120.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113557-76051.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113556-83666.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113557-30910.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113557-20233.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113557-38222.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113558-33354.png)
当且仅当x=1,f(x)max=f(1)=
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113555-86044.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113555-78584.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113555-86044.png)
(2)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113556-72447.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113556-16120.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113558-43046.png)
f(x)存在递减区间,
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113556-10443.png)
ax2+2x-1>0有x>0的解…………7分
a>0,显然满足…………9分
a<0时,则△=4+4a>0且ax2+2x-1=0至少有一个正根,此时-1<a<0……11分
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113556-10443.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113555-55531.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113555-59624.png)
核心考点
试题【(12分)已知函数f(x)=lnx-(a≠0)(1)若a=3,b=-2,求f(x)在[,e]的最大值;(2)若b=2,f(x)存在单调递减区间,求a的范围.】;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/20191018/20191018113532-45424.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113532-18431.png)
(Ⅰ)求
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113532-50342.png)
(Ⅱ)求函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113532-28259.png)
(Ⅲ)若直线
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113533-26045.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113533-42701.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113533-70064.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113510-67351.png)
(1)设曲线
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113510-51211.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113510-54614.png)
① 求
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113511-12539.png)
② 若数列
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113511-85785.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113511-60510.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113511-64881.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113511-81283.png)
求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113511-54351.png)
(2)设方程
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113511-40408.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113512-17307.png)
求证:对任意
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113512-87241.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113512-98726.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113512-62375.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113454-27167.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113454-27796.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113454-69095.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113455-88840.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113455-13822.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113455-12867.png)
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113436-85760.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113436-36706.png)
(1)当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113437-86519.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113437-39301.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113437-89581.png)
(2)求函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113437-39301.png)
(3)若在
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113437-33663.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113438-52043.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113438-46491.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113424-89308.png)
(Ⅰ)当a=﹣2时,求函数f(x)的单调区间;
(Ⅱ)若g(x)=
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113425-57620.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113425-15281.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113425-61713.png)
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