题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206074807-79928.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206074807-36790.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206074808-47011.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206074807-79928.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206074808-73433.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206074808-35720.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206074808-74247.png)
(1)求
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206074809-24285.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206074809-23011.png)
(2)设函数
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206074809-65759.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206074810-91555.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206074809-65759.png)
(3)设
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206074810-70153.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206074810-90256.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206074810-66991.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206074810-13476.png)
(2)
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206074809-65759.png)
(3)当
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206074811-24476.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206074810-66991.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206074811-64924.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206074810-66991.png)
解析
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206074807-79928.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206074808-35720.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206074807-79928.png)
(2)由(1)得,
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206074811-31310.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206074811-53645.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206074812-25421.png)
(3)比较复杂,先分
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206074812-68886.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206074812-37092.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206074812-81949.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206074813-54604.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206074810-66991.png)
解:(1)由
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206074808-74247.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206074813-84577.png)
∵1和
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206074808-35720.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206074808-74247.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206074813-11530.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206074813-18378.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206074810-13476.png)
(2)∵ 由(1)得,
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206074811-31310.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206074813-42499.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206074814-35157.png)
∵当
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206074814-86892.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206074814-98452.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206074814-77240.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206074815-66821.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206074815-35242.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206074809-65759.png)
∵当
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206074814-77240.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206074815-24252.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206074815-66821.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206074815-40254.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206074809-65759.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206074809-65759.png)
(3)令
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206074816-60963.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206074816-88500.png)
先讨论关于
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206074812-81949.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206074813-54604.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206074816-54540.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206074812-68886.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206074816-73974.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206074816-54259.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206074817-46096.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206074812-37092.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206074817-44128.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206074817-44515.png)
∴一2 , -1,1 ,2 都不是
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206074813-54604.png)
由(1)知
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206074818-13088.png)
① 当
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206074818-47604.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206074818-58991.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206074816-54259.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206074818-68012.png)
此时
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206074813-54604.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206074819-68915.png)
② 当
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206074819-12637.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206074818-58991.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206074816-54259.png)
又∵
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206074819-83434.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206074819-37801.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206074819-39729.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206074813-54604.png)
同理,
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206074813-54604.png)
③ 当
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206074820-65383.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206074820-82406.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206074816-54259.png)
又∵
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206074820-24307.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206074819-83434.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206074819-39729.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206074813-54604.png)
因此,当
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206074812-68886.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206074813-54604.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206074820-66914.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206074821-90784.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206074812-37092.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206074813-54604.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206074821-56807.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206074821-92072.png)
现考虑函数
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206074810-66991.png)
( i )当
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206074811-24476.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206074821-77677.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206074822-55259.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206074822-69313.png)
而
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206074822-44499.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206074822-80502.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206074810-66991.png)
( 11 )当
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206074811-64924.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206074821-77677.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206074823-83565.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206074823-74754.png)
而
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206074823-41466.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206074810-66991.png)
综上所述,当
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206074811-24476.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206074810-66991.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206074811-64924.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206074810-66991.png)
【考点定位】本题综合考查导数的定义、计算及其在求解函数极值和最值中的应用,考查较全面系统,要注意变形的等价性和函数零点的认识、极值和极值点的理解。本题主要考查数形结合思想和分类讨论思想,属于中高档试题,难度中等偏上,考查知识比较综合,全方位考查分析问题和解决问题的能力,运算量比较大。
核心考点
试题【若函数在处取得极大值或极小值,则称为函数的极值点。已知是实数,1和是函数的两个极值点.(1)求和的值;(2)设函数的导函数,求的极值点;(3)设,其中,求函数的】;主要考察你对函数的表示方法等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206074749-96342.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206074749-28710.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206074749-67022.png)
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206074723-88410.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206074724-45007.jpg)
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206074654-44691.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206074654-97253.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206074655-71592.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206074655-67910.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206074648-86590.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206074648-41379.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206074649-14820.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206074649-15573.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206074649-74499.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206074648-86590.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206074649-17823.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206074650-49597.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206074637-43372.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206074637-40748.png)
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