题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018131122-47174.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018131122-17291.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018131122-82342.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018131123-22422.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018131123-72445.png)
(I)求
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018131123-83333.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018131123-36513.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018131124-75632.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018131124-99453.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018131129-36153.png)
(III)若二次函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018131122-82342.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018131123-83333.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018131129-80337.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018131130-11988.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018131123-83333.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018131130-92408.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018131130-25711.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018131130-99156.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018131131-90114.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018131130-92408.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018131131-78577.png)
答案
解:(I)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018131131-95126.png)
可得
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018131131-11905.png)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018131122-82342.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018131132-53547.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018131132-28400.png)
令
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018131132-62691.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018131132-12761.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018131132-80265.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018131123-83333.png)
![]() | (0,![]() | ![]() | (![]() ![]() |
![]() | + | 0 | - |
![]() | 增函数 | 极大值 | 减函数 |
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018131123-83333.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018131133-34206.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018131123-83333.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018131133-34206.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018131133-29768.png)
(II)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018131133-77968.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018131133-70591.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018131133-34206.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018131134-27375.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018131134-41487.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018131134-64048.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018131135-64550.png)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018131134-64048.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018131135-48778.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018131135-46390.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018131135-76972.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018131135-21224.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018131136-29723.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018131135-76972.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018131136-13486.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018131136-86856.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018131136-29177.png)
(III)证明:若二次函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018131137-39639.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018131137-67194.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018131137-31165.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018131137-32047.png)
令
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018131138-82906.png)
由(I)知
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018131123-83333.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018131138-30321.png)
故
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018131138-22162.png)
取
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018131138-61483.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018131139-25448.png)
所以存在
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018131139-24067.png)
即存在
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018131139-15031.png)
所以函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018131123-83333.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018131139-43848.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018131140-76759.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018131140-17792.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018131140-24114.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018131139-43848.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018131132-12761.png)
解析
核心考点
试题【.已知定义在R上的二次函数满足,且的最小值为0,函数,又函数。(I)求的单调区间; (II)当≤时,若,求的最小值;(III)若二次函数图象过(4,2)点,对于】;主要考察你对函数的单调性与导数等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018131112-29412.png)
(1)当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018131113-35616.png)
(2)若函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018131113-26550.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018131052-87625.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018131052-85452.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018131053-34219.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018131053-63165.png)
①函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018131053-20717.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018131053-12647.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018131053-20717.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018131053-32930.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018131054-98885.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018131054-40197.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018131053-34219.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018131054-60934.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018131054-86845.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018131054-10392.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018131055-40095.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018131053-20717.png)
A.①③④ | B.①②③ | C.①④ | D.③④ |
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018131040-71417.png)
(1)试确定
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018131040-42987.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018131040-62815.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018131041-33836.png)
(2)求
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018131040-62815.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018131041-42314.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018131022-98805.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018131022-16618.png)
(1)若
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018131022-44871.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018131022-23497.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018131022-16618.png)
(2)讨论函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018131022-23497.png)
(
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018131022-94637.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018131023-18592.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018131023-61521.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018131023-65911.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018131022-16618.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018130953-52359.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018130953-18543.png)
(1)当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018130954-73940.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018130954-68783.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018130954-28835.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018130954-84377.png)
(2)若函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018130955-14429.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018130955-22834.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018130955-83867.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018130955-72370.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018130955-75682.png)
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