题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018064507-88206.gif)
(I)当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018064507-46555.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018064508-14811.gif)
(II)设|MN|=
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018064508-14258.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018064508-14258.gif)
(III)在(II)的条件下,若对任意的正整数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018064508-12420.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018064508-72250.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018064508-94565.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018064508-37139.gif)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018064508-38479.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018064508-89982.gif)
(Ⅲ)m的最大值为6
解析
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018064508-49345.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018064509-11267.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018064509-53003.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018064508-14811.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018064508-38479.gif)
(II)设M、N两点的横坐标分别为
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018064509-12581.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018064509-97092.gif)
|
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018064509-83916.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018064510-95390.gif)
由(1)、(2),可得
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018064510-77260.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018064510-81290.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018064510-45292.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018064510-84034.gif)
把(*)式代入,得
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018064511-12431.gif)
因此,函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018064511-49552.gif)
(III)易知
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018064511-15715.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018064511-37567.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018064512-56789.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018064512-52353.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018064512-42903.gif)
由于m为正整数,
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018064512-48436.gif)
又当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018064512-35131.gif)
因此,m的最大值为6.
核心考点
试题【已知函数的两条切线PM、PN,切点分别为M、N.(I)当时,求函数的单调递增区间;(II)设|MN|=,试求函数的表达式;(III)在(II)的条件下,若对任意】;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/20191018/20191018064501-71784.gif)
(1)若h(x)=f(x)-g(x)存在单调增区间,求a的取值范围;
(2)是否存在实数a>0,使得方程
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018064501-48806.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018064501-32497.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018064453-77557.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018064453-20557.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018064453-27356.gif)
(Ⅰ)求
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018064454-91305.gif)
(Ⅱ)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018064454-31749.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018064442-72490.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018064442-53421.gif)
(1)当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018064442-49338.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018064442-96879.gif)
(2)讨论函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018064443-96319.gif)
(3)(理做文不做)若
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018064443-90882.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018064443-37735.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018064443-54380.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018064430-66753.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018064430-64662.gif)
(1)若
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018064430-18337.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018064431-60687.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018064431-48794.gif)
(2)若
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018064430-18337.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018064431-63680.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018064431-42764.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018064432-75714.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018064423-39551.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018064423-76770.gif)
(1)求函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018064423-75850.gif)
(2)若函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018064423-75850.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018064423-88606.gif)
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