题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105821-49373.png)
(1)若
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105821-42423.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105822-76979.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105822-95743.png)
(2)若
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105821-42423.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105822-95743.png)
(3)设
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105822-58103.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105822-79955.png)
求证:①
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105822-13590.png)
求证:②
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105823-14137.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105823-75716.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105823-44673.png)
解析
(1)先求函数的导函数,根据若x=
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105823-34277.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105823-34277.png)
(2)f(x)在其定义域内为增函数可转化成只需在(0,+∞)内有2x2+ax+1≥0恒成立,建立不等关系,解之即可;
(3)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105824-89739.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105822-79955.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105824-17635.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105824-89474.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105824-81687.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105825-50880.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105825-81648.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105825-94556.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105825-70037.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105825-99216.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105826-34153.png)
解:(1)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105826-88744.png)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105821-42423.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105822-76979.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105826-97858.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105823-75716.png)
(2)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105821-42423.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105826-83509.png)
要
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105821-42423.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105827-98508.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105826-83509.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105827-78880.png)
而
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105827-82941.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105823-44673.png)
(3)①
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105824-89739.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105822-79955.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105824-17635.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105824-89474.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105824-81687.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105825-50880.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105825-81648.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105825-94556.png)
而
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105827-80539.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105822-13590.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105826-83509.png)
因此
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105828-29963.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105828-49320.png)
②
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105825-70037.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105825-99216.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105826-34153.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105828-56528.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105828-69337.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105829-81744.png)
=
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105829-33507.png)
=
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105829-65080.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105829-39847.png)
核心考点
试题【(本小题满分14分)设函数。 (1)若在处取得极值,求的值;(2)若在定义域内为增函数,求的取值范围;(3)设,当时,求证:① 在其定义域内恒成立;求证:② 。】;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
已知函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105810-10950.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105810-35471.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105810-78681.png)
(Ⅰ)求实数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105811-83921.png)
(Ⅱ)若
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105811-65859.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105811-13519.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105811-43726.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105749-25906.png)
(1)当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105749-89650.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105749-99304.png)
(2)令
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105749-29721.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105750-40325.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105750-41925.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105750-62013.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105750-85233.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105751-33399.png)
(3)当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105751-35928.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105751-21042.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105751-75770.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105751-89857.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105738-85170.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105738-64918.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105738-77174.png)
(1)求m的值。
(2)若
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105739-94161.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105739-85586.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105739-25269.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105727-48063.png)
(1)求函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105728-90809.png)
(2)若
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105728-29387.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105728-46746.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105728-62028.png)
(3)若
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105728-79906.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105728-33952.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105710-22777.png)
(I)如果函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105710-30779.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105711-60750.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105710-30779.png)
(II)在(Ⅰ)的条件下,求函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105711-60292.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105711-98089.png)
(III)若不等式
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105711-86451.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105712-36103.png)
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