题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017153437-24940.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017153438-64063.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017153438-35139.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017153438-33270.png)
(1)讨论函数
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017153438-32409.png)
(2)证明:若
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017153439-36575.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017153439-47930.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017153439-36535.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017153439-42136.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017153440-21490.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017153439-47930.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017153440-75100.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017153439-36535.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017153440-89710.png)
答案
解析
(1)先求解定义域,然后对于参数a进行讨论得到单调性的问题。
(2)由于不等式恒成立只要证明是单调增函数即可,因此利用构造函数的思想来证明得到。
解:(1)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017153438-32409.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017153440-21490.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017153440-11950.png)
(i)若
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017153440-95888.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017153441-62758.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017153441-97000.png)
故
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017153438-32409.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017153440-21490.png)
(ii)若
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017153441-81148.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017153441-49003.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017153442-33225.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017153442-48604.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017153442-68773.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017153442-62041.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017153443-47550.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017153443-34802.png)
故
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017153438-32409.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017153443-47808.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017153443-76109.png)
(iii)若
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017153443-76328.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017153444-87127.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017153438-32409.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017153444-75388.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017153444-58518.png)
(II)考虑函数
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017153444-22103.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017153445-90329.png)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017153445-22581.png)
由于1<a<5,故
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017153445-47242.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017153445-23599.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017153446-44991.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017153446-73817.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017153440-89710.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017153446-61530.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017153446-71526.png)
核心考点
举一反三
A.4 | B.5 | C.6 | D.7 |
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017153317-14589.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017153317-64472.png)
(1)当
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017153317-23196.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017153317-41175.png)
(2)求
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017153318-82195.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017153254-19517.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017153254-40488.png)
(1)若
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017153254-68080.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017153255-12140.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017153255-90593.png)
(2)若函数
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017153255-80447.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017153255-98057.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017153256-90050.png)
速v(千米/小时)需遵循的关系是
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017153257-50058.png)
规定
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017153257-65707.png)
(1)当
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017153258-62906.png)
(2)设机动车每小时流量
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017153258-22125.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017152546-34946.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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