题目
题型:不详难度:来源:
(1)当a=
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024900-21855.png)
(2)当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024900-50062.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024900-62394.png)
(3)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024900-75973.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024900-93232.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024900-63529.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024900-61333.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024901-53767.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024901-60888.png)
解析
试题分析:
(1)函数f(x)是二次与对数的结合,求单调性可以利用导数,以此先求定义域,求导,求导函数大于0与小于0分别求出单调递增与单调递减区间.
(2)要使得函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024900-63529.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024901-87264.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024901-94825.png)
不等式
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024901-57418.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024901-99348.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024902-52799.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024901-94825.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024902-52799.png)
(3)考虑把不等式两边
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024902-77155.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024902-85551.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024902-97786.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024902-22584.png)
试题解析:
(1)当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024903-14159.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024903-28353.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024903-36024.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024903-18402.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024903-36024.png)
由
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024903-82465.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024904-29953.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024904-86526.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024904-76724.png)
故函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024900-63529.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024900-61333.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024901-53767.png)
(2)因函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024900-63529.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024901-87264.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024901-94825.png)
不等式
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024901-57418.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024904-17299.png)
设
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024904-20528.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024905-57244.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024905-69063.png)
由
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024905-55049.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024905-69100.png)
(ⅰ)当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024905-19125.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024906-17444.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024906-45073.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024906-12358.png)
函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024906-70973.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024907-96407.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024907-56125.png)
(ⅱ)当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024907-31862.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024907-83671.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024901-94825.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024907-50950.png)
①
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024908-79280.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024908-83020.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024907-96407.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024908-93750.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024906-70973.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024907-96407.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024906-70973.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024908-56436.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024909-68572.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024909-91536.png)
②若
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024909-69020.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024909-72731.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024906-70973.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024909-19889.png)
在区间
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024910-95045.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024906-70973.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024908-56436.png)
(ⅲ)当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024910-81133.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024910-92355.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024901-94825.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024910-24998.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024906-12358.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024906-70973.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024908-56436.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024907-56125.png)
综上所述,实数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024910-67660.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024901-60888.png)
(3)据(2)知当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024905-19125.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024911-69079.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024908-56436.png)
(或另证
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024911-69079.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024911-32298.png)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024902-22584.png)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024911-78188.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024911-26324.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024912-91361.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024912-33238.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024912-85424.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024912-10487.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024913-40682.png)
核心考点
试题【已知函数f(x)=ax2+ln(x+1).(1)当a=时,求函数f(x)的单调区间;(2)当时,函数y=f(x)图像上的点都在所表示的平面区域内,求实数a的取值】;主要考察你对常见函数的导数等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024847-14275.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024847-83694.png)
(1)当a=2时,对任意的
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024847-82350.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024847-88606.png)
(2)若存在
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024848-61352.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024833-85782.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024833-31587.png)
(1)当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024833-42584.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024833-31925.png)
(2)设函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024834-27251.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024834-50372.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024834-56654.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024834-43875.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024834-77686.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024834-57022.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024834-76131.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024834-72071.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024834-50372.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024834-43875.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024835-47594.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024835-20394.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024834-50372.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024835-47594.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024834-43875.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024835-20394.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024821-89091.png)
(1)若
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024821-61210.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024821-42061.png)
(2)若
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024821-58419.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024821-42061.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024822-84448.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024811-96245.png)
(1)求
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024811-73061.png)
(2)当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024811-58565.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024811-43306.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024812-92190.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024812-49018.png)
(3)证明:当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024812-32471.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024812-90067.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024756-43757.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024756-39592.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024756-74303.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024757-81096.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024757-95878.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024757-77535.png)
(1)求
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024757-79931.png)
(2)求
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024758-92913.png)
(3)设
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024758-94645.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024758-33414.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024758-25364.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024758-97678.png)
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