题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204230906-46668.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204230907-40785.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204230907-18270.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204230907-33640.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204230907-84232.png)
(Ⅰ)求函数的解析式;
(Ⅱ)试证明函数
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204230907-64200.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204230907-24949.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204230908-70470.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204230908-53788.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204230908-29026.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204230908-63468.png)
(Ⅲ)试讨论这个函数的单调性,并求它的最大值、最小值,在给出的坐标系(见答题卡)中画出能体现主要特征的图简;
(Ⅳ)求不等式
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204230908-47564.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204230909-39706.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204230908-63468.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204230909-35386.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204230909-24572.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204230909-37937.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204230910-20808.png)
解析
试题分析:(1)由奇函数
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204230907-40785.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204230910-51684.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204230910-18412.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204230907-84232.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204230910-35749.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204230909-39706.png)
(2)设
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204230910-75570.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204230911-15568.png)
这样就有
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204230911-52201.png)
即函数
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204230908-70470.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204230907-24949.png)
对于函数
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204230908-70470.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204230908-53788.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204230908-29026.png)
设
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204230911-79231.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204230911-64652.png)
这样,欲使
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204230911-97720.png)
须使
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204230912-91599.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204230912-86622.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204230912-17604.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204230908-70470.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204230908-53788.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204230908-63468.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204230909-35386.png)
(3)由(2)可知函数
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204230908-70470.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204230912-74865.png)
由奇函数可知道,函数
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204230908-70470.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204230912-42060.png)
那么,在区间
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204230913-54273.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204230913-15651.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204230913-50330.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204230913-77914.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204230913-89884.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204230908-70470.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204230913-54273.png)
这样,就有
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204230914-14530.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204230914-92864.png)
图像如下所示. (3分)
(4)因为
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204230914-60355.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204230914-58319.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204230908-70470.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204230913-54273.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204230908-47564.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204230914-21890.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204230915-23823.png)
它的解集为
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204230915-95884.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204230915-51597.png)
点评:(1)若f(x)是奇函数,且在x=0处有定义,则f(0)一定为0.(2)用定义法证明函数的单调性的步骤:一设二作差三变形四判断符号五得出结论,其中最重要的是四变形,最好变成几个因式乘积的形式,这样便于判断符号。(3)解
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204230908-47564.png)
核心考点
试题【已知定义在实数集上的奇函数(、)过已知点.(Ⅰ)求函数的解析式;(Ⅱ)试证明函数在区间是增函数;若函数在区间(其中)也是增函数,求的最小值;(Ⅲ)试讨论这个函数】;主要考察你对函数的相关概念等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204230849-46269.png)
A.![]() ![]() | B.![]() ![]() |
C.![]() ![]() | D.![]() ![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204230837-65459.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204230837-52566.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204230837-75201.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204230837-80010.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204230824-19230.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204230824-88738.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204230824-94264.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204230824-94264.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204230824-96752.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204230825-96391.png)
(3)当
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204230825-49206.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204230824-94264.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204230825-24455.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204230825-99554.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204230825-82272.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204230826-76647.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204230826-21230.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204230826-79064.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204230818-88874.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204230819-10605.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204230819-96717.jpg)
①
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204230819-92439.png)
②
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204230819-15835.png)
③
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204230820-82509.png)
④
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204230820-29428.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204230820-84659.png)
⑤
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204230820-29428.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204230820-84659.png)
A.①③ | B.①③④ | C.②④ | D.②⑤ |
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204230715-35841.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204230715-17061.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204230716-63973.png)
(I)写出年利润
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204230716-66494.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204230715-35841.png)
(Ⅱ)年生产量为多少千件时,该公司在这一品牌服装的生产中所获年利润最大?
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