题目
题型:不详难度:来源:
(I)讨论f(x)的单调性;
(Ⅱ)若x≥1时,
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051514-16677.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051514-87628.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051514-31826.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051514-44760.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051515-25053.png)
解析
试题分析:解:(Ⅰ)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051514-87628.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051515-43225.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051515-57051.png)
①当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051515-94556.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051516-10280.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051514-87628.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051515-43225.png)
②当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051516-72601.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051516-10280.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051516-12499.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051516-48037.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051516-33429.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051514-87628.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051514-31826.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051514-44760.png)
(Ⅱ)由题意,
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051517-58232.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051517-92026.png)
设
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051517-33606.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051517-34894.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051517-58232.png)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051517-15018.png)
①当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051515-94556.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051518-45251.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051518-55470.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051518-68047.png)
∴当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051518-86928.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051519-93470.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051517-34894.png)
②当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051516-72601.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051519-95468.png)
(ⅰ)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051519-65116.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051515-25053.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051519-23791.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051518-55470.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051518-68047.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051519-43808.png)
(ⅱ)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051520-91779.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051520-20937.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051520-25152.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051520-64502.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051520-27614.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051521-12780.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051518-45251.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051518-55470.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051519-93470.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051517-34894.png)
综上,实数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051521-86329.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051521-62374.png)
另解:
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051517-58232.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051517-92026.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051521-27834.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051518-86928.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051522-29554.png)
设
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051522-19426.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051522-22390.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051522-29834.png)
又由洛必达法则知,
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051522-82028.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051523-24889.png)
故,
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051515-25053.png)
点评:导数常应用于求曲线的切线方程、求函数的最值与单调区间、证明不等式和解不等式中参数的取值范围等。
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051505-48977.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051505-68987.png)
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051459-18936.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051500-29146.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051500-83753.png)
A.充分不必要 | B.必要不充分 | C.充要 | D.既不充分也不必要 |
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051453-20921.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051447-76885.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051441-34465.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051441-49725.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051442-15334.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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