题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040446-85347.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040446-99507.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040446-83740.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040446-73803.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040447-69404.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040447-39634.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040447-37295.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040447-34240.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040448-69696.png)
(1)当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040448-77796.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040448-69696.png)
(2)当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040448-43449.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040448-45728.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040448-70196.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040449-64083.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040449-90745.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040449-62803.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040449-90745.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040449-61982.png)
(2)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040450-11340.png)
解析
试题分析:本题考查导数的运算,利用导数研究函数的单调性、最值等基础知识,考查函数思想、分类讨论思想、化归与转化思想.第一问,数形结合得到
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040449-90745.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040450-77013.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040449-90745.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040450-15683.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040450-50475.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040449-90745.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040450-68424.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040451-20509.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040449-90745.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040451-90669.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040451-81787.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040449-90745.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040451-98077.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040450-68424.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040452-56902.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040451-20509.png)
试题解析:(I) 因为
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040452-84646.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040452-81760.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040452-17310.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040452-54884.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040453-67108.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040453-16818.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040453-38625.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040453-40912.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040454-76223.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040454-68259.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040454-68207.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040454-10464.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040454-37956.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040455-46003.png)
令
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040455-43913.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040455-73684.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040454-68259.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040455-16199.png)
令
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040456-97997.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040456-64430.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040454-68259.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040456-69003.png)
综上,
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040454-68259.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040454-68207.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040455-16199.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040454-68259.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040456-69003.png)
(II)因为
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040452-84646.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040452-81760.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040456-59979.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040456-65771.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040457-46016.png)
因为
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040457-65663.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040457-16246.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040454-68259.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040457-14441.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040457-76172.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040458-96915.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040458-86228.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040458-74249.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040458-53818.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040459-70875.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040459-56010.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040459-61129.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040454-68259.png)
所以当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040459-25760.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040454-68259.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040500-23119.png)
令
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040500-67948.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040500-54386.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040459-70875.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040500-54031.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040500-44171.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040459-56010.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040501-22645.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040454-68259.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040501-22238.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040501-44635.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040454-68259.png)
所以当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040458-74249.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040454-68259.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040501-50602.png)
令
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040502-58241.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040502-78549.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040502-24286.png)
综上所述,
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040450-11340.png)
核心考点
试题【已知函数,点为一定点,直线分别与函数的图象和轴交于点,,记的面积为.(1)当时,求函数的单调区间;(2)当时, 若,使得, 求实数的取值范围.】;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/20191018/20191018040437-53546.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040438-50124.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040438-66158.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040438-46870.png)
(1)求
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040438-90001.png)
(2)讨论
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040438-31790.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040438-31790.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040427-83162.png)
(Ⅰ)讨论函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040427-92140.png)
(Ⅱ)设
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040427-81160.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040427-51113.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040427-62917.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040428-12791.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040411-36280.png)
(1)若存在
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040411-66424.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040412-97703.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040412-44388.png)
(2)求证:当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040412-44418.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040412-54393.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040400-50292.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040401-58083.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040401-78150.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040401-65086.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040400-50292.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040401-58083.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040401-25726.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040401-48783.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040402-29502.png)
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040348-56851.png)
(1)当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040349-98039.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040349-75621.png)
(2)若当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040349-24892.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040349-97977.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018040350-86888.png)
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