已知函数

(1)求函数

的单调区间;
(2)若函数

的图像与直线

恰有两个交点,求

的取值范围.
(1)因为
令

得
由

时,

在

根的左右的符号如下表所示
所以

的递增区间为

的递减区间为
(2)由(1)得到

,

要使

的图像与直线

恰有两个交点,只要

或

,
即

或

.
练习册系列答案
相关习题
科目:高中数学
来源:不详
题型:解答题
设函数

>

,
(1) 求函数

的极大值与极小值;
(2) 若对函数的

,总存在相应的

,使得

成立,求实数a的取值范围.
查看答案和解析>>
科目:高中数学
来源:不详
题型:填空题
函数

在

上是增函数的一个充分非必要条件是
.
查看答案和解析>>
科目:高中数学
来源:不详
题型:填空题
给出下列命题:
①已知函数

在点

处连续,则

;
②若不等式

对于一切非零实数

均成立,则实数

的取值范围是

③不等式

的解集是

④如果

的三个内角的余弦值分别等于

的三个内角的正弦值,则

为
锐角三角形,

为钝角三角形.其中真命题的序号是
(将所有真命题的序号都填上)
查看答案和解析>>
科目:高中数学
来源:不详
题型:单选题

若函数

是定义在

上的偶函数,且在

上单调递减,则( ).
查看答案和解析>>