题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017133633-12720.png)
(Ⅰ)当
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017133633-30179.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017133633-62662.png)
(Ⅱ)若
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017133634-73571.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017133634-73571.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017133634-79371.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017133634-92432.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017133634-19106.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017133633-62662.png)
(Ⅱ)实数
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017133634-92432.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017133634-61514.png)
解析
试题分析:(Ⅰ)由
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017133633-30179.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017133635-93171.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017133635-51597.png)
由
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017133635-94844.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017133635-47162.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017133636-52212.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017133636-50975.png)
由
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017133636-46789.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017133636-32202.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017133636-52212.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017133636-49434.png)
所以函数有最小值
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017133634-19106.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017133633-62662.png)
(Ⅱ)由
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017133637-67536.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017133637-33168.png)
于是
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017133634-79371.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017133634-73571.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017133637-85663.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017133637-49976.png)
由
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017133638-24711.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017133638-77172.png)
①当
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017133638-67422.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017133638-18134.png)
此时
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017133636-52212.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017133638-56446.png)
故
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017133639-35179.png)
②当
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017133639-76600.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017133639-49111.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017133639-32244.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017133639-58750.png)
![]() | ![]() | ![]() | ![]() |
![]() | ![]() | ![]() | ![]() |
![]() | 单调递减 | 极小值 | 单调递增 |
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017133638-56446.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017133641-83309.png)
依题意,
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017133641-97017.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017133642-76107.png)
综合①,②得,实数
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017133634-92432.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017133634-61514.png)
点评:典型题,本题属于导数应用中的基本问题,通过研究函数的单调性,明确了极值情况。涉及不等式恒成立问题,转化成了研究函数的单调性及最值,得到求证不等式。
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017133627-23954.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017133628-38813.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017133628-93638.png)
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017133623-81123.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017133623-65509.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017133623-81123.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017133623-87262.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017133623-52399.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017133624-62007.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017133617-36824.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017133617-96025.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017133617-70451.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017133617-22448.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017133618-95403.png)
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017133611-45277.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017133611-85210.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017133611-83878.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017133612-52229.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017133549-88402.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017133549-22475.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017133549-87783.png)
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