1 . 已知函数
.
(1)求函数
的最大值及相应
的取值;
(2)方程
在
上有且只有一个解,求实数
的取值范围;
(3)是否存在实数
满足对任意
,都存在
,使
成立.若存在,求
的取值范围;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38dc58c3df4680b04ac80da3b3e0a1a8.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9c0d827ef8598ba6b70b34b2bdcd1e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18c9aeed3c8c5a04e48d011c607f9142.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(3)是否存在实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4317afae8118bfc41f443e7f18f417ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33890c6b0bf167514d44139d9dca0154.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b2927014825940051c10ae87442cf11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
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解题方法
2 . 已知函数
,
.
(1)求不等式
的解集;
(2)若
有两个不同的实数根,求a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fa644ce4fd69670b1da5314ba0c3902.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0374ece448bd4d63978c2f31bd75a0fe.png)
(1)求不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb584bbe5dbf0438934967b942521013.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea1b48323f7fc70e4acab208735c5238.png)
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