题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017135404-46505.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017135404-73285.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017135404-43772.png)
(1)求a,b满足的关系式;
(2)若
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017135405-73481.png)
(3)证明:
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017135405-28620.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017135405-35622.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017135405-48015.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017135406-56064.png)
解析
试题分析:(1)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017135406-72335.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017135406-89355.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017135405-48015.png)
(2)由(Ⅰ)知,
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017135406-43921.png)
令
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017135407-36133.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017135407-96900.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017135407-42320.png)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017135407-44725.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017135407-43021.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017135408-77579.png)
①当
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017135408-57320.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017135408-11783.png)
若
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017135408-83054.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017135408-54032.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017135409-46832.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017135409-17492.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017135409-94860.png)
即
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017135409-27780.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017135406-56064.png)
②
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017135409-42774.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017135410-78270.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017135410-70805.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017135410-17009.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017135409-46832.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017135406-56064.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017135410-74541.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017135410-57361.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017135409-27780.png)
综上所述,所求
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017135411-53515.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017135406-56064.png)
(3)有(2)知当
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017135411-47826.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017135411-91134.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017135411-26996.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017135411-66447.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017135412-26757.png)
令
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017135412-65011.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017135412-22511.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017135412-89092.png)
即
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017135413-54367.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017135413-56432.png)
上式中令n=1,2,3,…,n,并注意到:
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017135413-25225.png)
然后n个不等式相加得到
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017135413-51268.png)
点评:利用导数工具研究函数的有关性质,把导数应用于单调性、极值等传统、常规问题的同时,进一步升华到处理与不等式的证明、解析几何、方程的解及函数零点等问题,是函数知识和其它知识的交汇运用
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017135342-40142.png)
(Ⅰ)若
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017135343-20180.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017135343-94715.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017135343-27133.png)
(Ⅱ)若
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017135343-20180.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017135343-27133.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017135343-20180.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017135343-72116.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017135337-55239.png)
A.4x-y=0 | B.4x-y-4=0 | C.2x-y-2=0 | D.4x-y=0或4x-y-4=0 |
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017135322-29181.png)
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017135316-42385.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017135317-10118.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017135317-95129.png)
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