题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204202954-86814.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204202954-76029.png)
(1)求
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204202954-76029.png)
(2)判断
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204202954-95689.png)
(3)若对于区间 [3,4]上的每一个
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204202954-33286.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204202954-95689.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204202955-50241.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204202955-26912.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204202955-79095.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204202955-77696.png)
解析
试题分析:解:(1)∵
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204202954-86814.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204202956-41085.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204202954-95689.png)
即
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204202956-14801.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204202956-39162.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204202956-58838.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204202957-74315.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204202957-28945.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204202954-95689.png)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204202957-74544.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204202957-40138.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204202955-79095.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204202957-50558.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204202958-71478.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204202958-80363.png)
(2)由(1)得
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204202958-19349.png)
设1<x1<x2,则
f(x1)-f(x2)=log
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204202958-19271.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204202959-18522.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204202958-19271.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204202959-63148.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204202958-19271.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204202959-65935.png)
=log
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204202958-19271.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204202959-27079.png)
∵ 1<x1<x2,∴ x2-x1>0,
∴ (x1x2-1)+(x2-x1)>(x1x2-1)-(x2-x1)>0
即
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204202959-27079.png)
∴ f(x1)-f(x2)<0即f(x1)<f(x2),在(1,+∞)上是增函数 10分
(3)由(1),不等式
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204202954-95689.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204202955-50241.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204203000-72665.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204203000-97816.png)
由题意得对于区间[3,4]上的每一个
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204202954-33286.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204203000-72665.png)
令
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204203000-78969.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204203000-46808.png)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204203000-69860.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204202955-77696.png)
点评:解决的关键是对于函数奇偶性和单调性的灵活运用,以及利用分离参数的思想求解函数的最值得到范围。属于中档题。
核心考点
试题【)设为奇函数,为常数.(1)求的值;(2)判断在区间(1,+∞)内的单调性,并证明你的判断正确;(3)若对于区间 [3,4]上的每一个的值,不等式>恒成立】;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
(1)设在甲家租一张球台开展活动
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204202927-72182.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204202927-23866.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204202927-63081.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204202927-72182.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204202927-76794.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204202927-63081.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204202927-23866.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204202927-76794.png)
(2)问:小张选择哪家比较合算?为什么?
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204202822-77268.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204202822-99542.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204202822-58620.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204202822-80173.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204202823-35720.png)
(1)试问函数f(x)的图象上是否存在两个不同的点A,B,使直线AB恰好与y轴垂直,若存在,求出A,B两点的坐标;若不存在,请说明理由并加以证明.
(2)若
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204202823-53276.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204202823-93688.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204202823-89256.png)
求实数m的取值范围.
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204202721-82185.png)
(1)证明:对于一切的实数x都有f(x)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204202722-92783.png)
(2)若函数
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204202722-65675.png)
(3)证明:
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204202722-20622.png)
据调查统计,通过这两条公路从城市甲到城市乙的200辆汽车所用时间的频数分布如下表:
所用的时间(天数) | 10 | 11 | 12 | 13 |
通过公路1的频数 | 20 | 40 | 20 | 20 |
通过公路2的频数 | 10 | 40 | 40 | 10 |
(Ⅰ)为了尽最大可能在各自允许的时间内将货物运往城市乙,估计汽车A和汽车B应如何选择各自的路径;
(Ⅱ)若通过公路1、公路2的“一次性费用”分别为
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204202711-43517.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204202711-65733.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204202508-48394.png)
(1)当
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204202509-46664.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204202509-97369.png)
(2)若关于
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204202509-25489.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204202509-97381.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204202509-88143.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204202509-58104.png)
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