题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018103729-32752.png)
(Ⅰ)当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018103730-28549.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018103730-64343.png)
(Ⅱ)设函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018103730-64343.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018103730-28685.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018103730-50553.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018103730-48862.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018103730-48862.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018103731-39285.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018103731-67501.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018103731-67501.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018103731-38636.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018103730-64343.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018103731-53311.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018103731-13056.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018103732-26886.png)
解析
试题分析:(Ⅰ)当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018103730-28549.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018103732-53643.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018103732-23019.png)
所以,当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018103732-93655.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018103733-43424.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018103733-78096.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018103733-62083.png)
所以函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018103730-64343.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018103731-53311.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018103731-13056.png)
(Ⅱ)因为
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018103733-37789.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018103730-28685.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018103733-96498.png)
所以切线
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018103730-48862.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018103734-85742.png)
令
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018103734-16146.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018103734-42789.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018103730-50553.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018103734-29368.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018103731-67501.png)
只需
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018103735-98162.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018103735-83799.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018103730-50553.png)
令
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018103735-64919.png)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018103735-34916.png)
因为
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018103734-29368.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018103736-56915.png)
①若
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018103736-56011.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018103732-26886.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018103736-64604.png)
所以,当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018103736-79668.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018103736-74560.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018103737-28948.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018103737-98354.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018103737-25113.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018103732-26886.png)
②若
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018103737-67810.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018103738-37639.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018103738-82615.png)
所以,当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018103736-79668.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018103738-96447.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018103737-28948.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018103737-98354.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018103738-80951.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018103738-37639.png)
③若
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018103739-85671.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018103739-23334.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018103739-34595.png)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018103739-98691.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018103740-16989.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018103737-28948.png)
![]() | ![]() | ![]() | ![]() |
![]() | ![]() | 0 | ![]() |
![]() | 递减 | 极小值 | 递增 |
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018103741-54815.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018103739-23334.png)
综合①②③,可得,当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018103732-26886.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018103741-11955.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018103730-50553.png)
此时点
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018103731-67501.png)
点评:导数是研究函数性质的有力工具,求解函数单调性、极值、最值时,不要漏掉函数的定义域,另外,一般含参数的问题离不开分类讨论,分类讨论时要做到分类标准不重不漏.
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018103716-32358.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018103717-49916.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018103717-45295.png)
(1)求函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018103717-83107.png)
(2)若
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018103717-83107.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018103717-83976.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018103718-21841.png)
(3)在(2)的条件下,证明:
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018103718-77984.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018103704-54959.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018103705-51463.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018103705-29118.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018103705-27442.png)
A.![]() | B.![]() |
C.![]() | D.不确定 |
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018103656-63476.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018103656-18789.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018103656-40547.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018103656-75272.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018103656-17205.png)
A.12 | B.13 | C.15 | D.16 |
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018103647-51403.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018103647-32075.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018103635-64322.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018103635-82774.png)
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