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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2 . 函数
定义在区间
,
,都有
,且
不恒为零.
求
的值;
若
且
,求证:
;
若
,求证:
在
上是增函数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d479a86a1711709b2d100fe4daf3e7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cead849c0dc4a82285808a7e081ad75c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c10570c017a8e9ced002591abf78bc2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf30188c22ac25070805524f9d3ecf33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d479a86a1711709b2d100fe4daf3e7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4141b26d2c32655003494a91ad6331b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cb07fc041df359b25b6b47bcc4d024e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65863c1abad833b79c303bfca24f535c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/388f328e3593af8891ace6e36aa00ec0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b329c4dda26555f33053b1d65e1f4c12.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/807aa53fc1daab149bd87713c378a055.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4bb89a362c1faf4d0c306eabbb59710.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d03939641eb640b6392f9e6f1b143be4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d479a86a1711709b2d100fe4daf3e7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cead849c0dc4a82285808a7e081ad75c.png)
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12-13高三上·上海闵行·期末
3 . 记函数
在区间D上的最大值与最小值分别为
与
.设函数
,
.
.
(1)若函数
在
上单调递减,求
的取值范围;
(2)若
.令
.
记
.试写出
的表达式,并求
;
(3)令
(其中I为
的定义域).若I恰好为
,求b的取值范围,并求
.
![](https://img.xkw.com/dksih/QBM/2012/1/11/1570683802361856/1570683807817728/STEM/9582e889d13842e4a2b52304ad335f7b.png?resizew=36)
![](https://img.xkw.com/dksih/QBM/2012/1/11/1570683802361856/1570683807817728/STEM/53f354149439482da1d81e60a86a9f15.png?resizew=124)
![](https://img.xkw.com/dksih/QBM/2012/1/11/1570683802361856/1570683807817728/STEM/60487e13589d4084be1cb28b17b5e125.png?resizew=120)
![](https://img.xkw.com/dksih/QBM/2012/1/11/1570683802361856/1570683807817728/STEM/6f2afa29c68d46ab88921ed94baa0081.png?resizew=164)
![](https://img.xkw.com/dksih/QBM/2012/1/11/1570683802361856/1570683807817728/STEM/c2183a799b544492b6776971b869a0c5.png?resizew=58)
![](https://img.xkw.com/dksih/QBM/2012/1/11/1570683802361856/1570683807817728/STEM/49eeef9ae20e455fb375f0dbbd9cf19a.png?resizew=167)
(1)若函数
![](https://img.xkw.com/dksih/QBM/2012/1/11/1570683802361856/1570683807817728/STEM/76ac75f86cd74dcf9d8acac87bc12c95.png?resizew=35)
![](https://img.xkw.com/dksih/QBM/2012/1/11/1570683802361856/1570683807817728/STEM/365e5307876349a09d5103890ca50a5a.png?resizew=32)
![](https://img.xkw.com/dksih/QBM/2012/1/11/1570683802361856/1570683807817728/STEM/be336b753bd144ea8f785d43a97a9ad3.png?resizew=13)
(2)若
![](https://img.xkw.com/dksih/QBM/2012/1/11/1570683802361856/1570683807817728/STEM/001344f6940a4163acd9f77fdd9d21cf.png?resizew=40)
![](https://img.xkw.com/dksih/QBM/2012/1/11/1570683802361856/1570683807817728/STEM/46c1243c1ae34ce9b43742c58f311d92.png?resizew=324)
记
![](https://img.xkw.com/dksih/QBM/2012/1/11/1570683802361856/1570683807817728/STEM/57f9462183dc4730be1b0bfbcdaf9bb3.png?resizew=161)
![](https://img.xkw.com/dksih/QBM/2012/1/11/1570683802361856/1570683807817728/STEM/59860422c5cf40d5be610ccd63219d14.png?resizew=33)
![](https://img.xkw.com/dksih/QBM/2012/1/11/1570683802361856/1570683807817728/STEM/9c6ceeb3217b452aac763d88c9ebd64c.png?resizew=128)
(3)令
![](https://img.xkw.com/dksih/QBM/2012/1/11/1570683802361856/1570683807817728/STEM/fe89ba8a284143018aca801659c743f1.png?resizew=332)
![](https://img.xkw.com/dksih/QBM/2012/1/11/1570683802361856/1570683807817728/STEM/eff96ecb4c384b07b7222437d08f0b68.png?resizew=55)
![](https://img.xkw.com/dksih/QBM/2012/1/11/1570683802361856/1570683807817728/STEM/eb3a591ebfb449fd9137aee39fe96be5.png?resizew=36)
![](https://img.xkw.com/dksih/QBM/2012/1/11/1570683802361856/1570683807817728/STEM/ae029b52880b4719b66451df4d7d0dc2.png?resizew=105)
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