题目
题型:不详难度:来源:
(1)求函数f(x)的解析式;
(2)求函数f(x)的单调增区间,并求函数f(x)在[-1,3]上的最大值和最小值.
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025146-32250.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025146-42193.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025147-70853.png)
解析
试题分析:(1)根据
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025147-72555.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025147-19096.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025147-21269.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025147-57640.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025148-18210.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025147-72555.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025148-53820.png)
试题解析:
解:(1)∵
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025147-72555.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025148-12415.png)
即
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025148-44630.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025147-19096.png)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025147-57640.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025149-18572.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025149-59882.png)
由题设知
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025147-21269.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025149-53508.png)
故
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025146-32250.png)
(2)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025149-92242.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025149-96879.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025150-39187.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025147-72555.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025150-22246.png)
∴函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025147-72555.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025150-84360.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025150-37749.png)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025151-30147.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025151-37640.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025151-51251.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025151-80688.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025146-42193.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025151-30773.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018025147-70853.png)
核心考点
试题【设f(x)=ax3+bx+c(a≠0)为奇函数,其图象在点(1,f(1))处的切线与直线x-6y-7=0垂直,导函数f′(x)的最小值为-12.(1)求函数f(】;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
(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.
![](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.![]() |
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