题目
题型:不详难度:来源:
已知函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060256-48567.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060256-79552.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060256-98392.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060257-30309.gif)
(Ⅰ) 当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060257-97888.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060257-98272.gif)
(Ⅱ) 设直线
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060257-30309.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060256-79552.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060257-45234.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060258-91641.gif)
求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060258-85241.gif)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060258-59703.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060258-29092.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060258-40443.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060259-55428.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060259-58532.gif)
(2)不妨设
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060259-85997.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060259-27653.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060300-86933.gif)
只需证
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060300-15392.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060300-52874.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060300-20789.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060300-80780.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060301-10423.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060301-46423.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060301-66987.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060301-63119.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060302-47502.gif)
令
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060302-57977.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060302-61775.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060302-33579.gif)
只需证
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060303-57114.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060303-21351.gif)
令
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060303-72147.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060303-36666.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060304-19743.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060302-33579.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060304-92457.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060304-34555.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060304-18016.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060304-37691.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060302-33579.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060305-26196.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060305-93257.gif)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060300-86933.gif)
解析
核心考点
试题【(本小题满分12分)已知函数的图象为曲线, 函数的图象为直线.(Ⅰ) 当时, 求的最大值;(Ⅱ) 设直线与曲线的交点的横坐标分别为, 且, 求证: .】;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
已知函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060246-83018.gif)
(1)求
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060247-28738.gif)
(2)若
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060247-53789.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060247-31509.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060247-87936.gif)
(3)已知
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060248-71466.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060248-23783.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060248-53842.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060235-36139.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060235-75240.gif)
(Ⅰ)若函数在区间
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060235-60526.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060235-59806.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060235-20203.gif)
(Ⅱ)如果当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060236-71420.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060236-97991.gif)
已知以函数f(x)=mx3-x的图象上一点N(1,n)为切点的切线倾斜角为
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060226-74001.gif)
(1)求m、n的值;
(2)是否存在最小的正整数k,使得不等式f(x)≤k-1995,对于x∈[-1,3]恒成立
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060226-59132.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060213-62874.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060213-62338.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060213-92799.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060213-70691.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060213-36399.gif)
(1)求函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060213-36399.gif)
(2)若
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060213-80414.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060213-10341.gif)
(3)若不等式
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060214-40583.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060214-40984.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060214-64884.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060214-71760.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060200-99545.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060201-43698.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060201-68233.gif)
(1)求实数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060201-81255.gif)
(2) 若关于
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060201-11989.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060201-10351.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060201-76500.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060201-98960.gif)
(3) 证明:
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060201-73840.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060202-62995.gif)
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