名校
1 . 设
是定义在
上的函数,若存在
,使得
在
单调递增,在
上单调递减,则称
为
上的单峰函数,
为峰点,包含峰点的区间称为含峰区间,其含峰区间的长度为:
.
(1)判断下列函数中,哪些是“
上的单峰函数”?若是,指出峰点;若不是,说出原因;
;
(2)若函数
是
上的单峰函数,求实数
的取值范围;
(3)若函数
是区间
上的单峰函数,证明:对于任意的
,若
,则
为含峰区间;若
,则
为含峰区间;试问当
满足何种条件时,所确定的含峰区间的长度不大于0.6.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4776c85b79df196f606d3ebf3697fbc3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85b7e150af2052a1664cde963273d905.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9a801780561c48c27b05e3894de99a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eae40787b884e40c9fbff558491372d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4776c85b79df196f606d3ebf3697fbc3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13502d46b8563c54c09b29b20b3006a4.png)
(1)判断下列函数中,哪些是“
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/304226ca50149b49702928e44d565964.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c29d3981fe4fc667bfc4b9ab72a0f938.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d99175f13f12333b9bf574b79cf38e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9210e75c35fb455d0446eb7ddba7d79c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/304226ca50149b49702928e44d565964.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa1825e7e125bba03a5617d0ebe2830.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5ce40da2cbd52723210bbfa98a7f81b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14283f108568721e6d9ec8d42036be33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25ba30f1aa5e75750c67b142fc1d7837.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f2a570f0086433e604736679f7192c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
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