题目
题型:不详难度:来源:
已知函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018144426-79389.gif)
(Ⅰ)求函数的定
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018144426-33680.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018144426-79389.gif)
(Ⅱ)若
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018144426-74639.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018144426-81068.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018144427-76330.gif)
(Ⅲ)当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018144427-94702.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018144427-28233.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018144427-56829.gif)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018144427-41291.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018144428-21263.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018144428-40831.gif)
∴ 函数的定义域为
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018144428-23593.gif)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018144428-21025.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018144429-37110.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018144426-79389.gif)
(Ⅱ)由
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018144426-74639.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018144426-81068.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018144429-22343.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018144429-96293.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018144426-74639.gif)
令
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018144429-45519.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018144426-74639.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018144429-38277.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018144430-56057.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018144426-74639.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018144430-54271.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018144430-90056.gif)
(Ⅲ)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018144430-76637.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018144430-28077.gif)
证法一:设函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018144431-28388.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018144431-52392.gif)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018144431-91707.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018144431-84457.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018144432-89503.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018144432-57932.gif)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018144432-60226.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018144432-91867.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018144432-91867.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018144433-37321.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018144433-83907.gif)
则当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018144433-66507.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018144433-18390.gif)
证法二:构造函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018144434-60237.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018144434-61210.gif)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018144434-36624.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018144434-17066.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018144434-92501.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018144435-47887.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018144435-47898.gif)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018144435-16095.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018144435-58913.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018144435-75008.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018144436-28438.gif)
解析
核心考点
试题【.(本小题满分14分)已知函数(Ⅰ)求函数的定义域,并证明在定义域上是奇函数;(Ⅱ)若恒成立,求实数的取值范围;(Ⅲ)当时,试比较与的大小关系】;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
已知
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018144246-15104.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018144247-14094.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018144247-12882.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018144247-17765.gif)
(Ⅰ)求
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018144247-25192.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018144247-54281.gif)
(Ⅱ)求
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018144248-69539.gif)
(Ⅲ)当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018144248-53104.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018144248-42443.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018144248-61025.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018144247-25192.gif)
设函数f(x)=x3+ax2+bx(x>0)的图象与直线y=4相切于M(1,4).
(Ⅰ)求f(x)=x3+ax2+bx在区间(0,4]上的最大值与
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018144158-88475.gif)
(Ⅱ)设存在两个不等正数s,t(s<t),当x∈[s,t]时,函数f(x)=x3+ax2+bx的值域是[ks,kt],求正数k的取值范围。
已知函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018144138-75066.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018144138-35882.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018144139-85217.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018144139-27594.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018144139-27111.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018144139-59662.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018144139-10024.gif)
(1) 试确定
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018144138-35882.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018144140-63020.gif)
(2) 若函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018144140-67979.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018144140-23105.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018144140-82302.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018144138-35882.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018144126-68505.gif)
A
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018144126-15933.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018144127-17760.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018144126-15933.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018144127-52684.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018144126-15933.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018144127-96903.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018144126-15933.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018144127-16173.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018144114-66438.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018144114-47004.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018144114-63473.gif)
A
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018144115-11296.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018144115-30615.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018144115-11296.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018144115-72503.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018144115-98836.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018144115-11296.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018144116-36634.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018144115-11296.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018144116-79962.gif)
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