名校
1 . 先看下面的阅读材料:已知三次函数
(
), 称相应的二次函数
为
的“导函数”,研究发现,若导函数
在区间
上恒成立,则
在区间
上单调递增;若导函数
在区间
上恒成立,则
在区间
上单调递减.例如:函数
,其导函数
,由
,得
, 由
,得
或
,所以三次函数
在区间
上单调递增,在区间
和
上单调递减. 结合阅读材料解答下面的问题:
(1)求三次函数
的单调区间;
(2)某市政府欲在文旅区内如图所示的矩形
地块中规划出一个儿童乐园(如图中阴影部分),形状为直角梯形
(线段
和
为两条底边,
),已知![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07160f14b3b453bebb64cb2bf96dc85a.png)
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f171567256d0e2b0a88e327d5006af9.png)
,其中曲线
是以
为顶点、
为对称轴的抛物线的一部分.
①设
,求出梯形
的面积
与
的解析式;
②求该公园的最大面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1cbb68078590e8785def6cb1d7e0126a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20849c00c47cbdc43f18d53341b6c4e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a4ea3d627afa62f550d2d9bf366728f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/732ab7a068ec2ea3615f0bcb33a68841.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00b0fdfd20a413cff3aae1b3fd3a3ab5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c44ad0bc2b7d218bae59f0cf856109ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f54af6661254f0b1a627c612827bb54.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/732ab7a068ec2ea3615f0bcb33a68841.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cafe647840cc2ace0d94bdca3c4fb03d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00b0fdfd20a413cff3aae1b3fd3a3ab5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7da6d82d173ad18cc040e94c925b5ab9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c0aa2ef928b6e3341d0a0dc6d8055b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27cf818dd484cc4cebd40a5f28eb8e9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70c82644f77c5455ceb7f94950e94273.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/879234adbae93aa72b7e101b3738d4e0.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/21/886ae69d-efe6-4b66-b763-aa1ceb6bd076.png?resizew=72)
(1)求三次函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b21ad3ae9e10266f6749c29d38b22801.png)
(2)某市政府欲在文旅区内如图所示的矩形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7517f54a1ccb77add90ade02b3a84719.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f90c780dac29ff8b7df5881d3b33abab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42af8cdea9c5269c17aebb086afdd136.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b27b89c70987f830a886400eafa3acd7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5fe30c67ac20cd4e8b9cc2d0d420a7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07160f14b3b453bebb64cb2bf96dc85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5fe30c67ac20cd4e8b9cc2d0d420a7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f171567256d0e2b0a88e327d5006af9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5fe30c67ac20cd4e8b9cc2d0d420a7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa2b5e09f8ec785c59900a529390a02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
①设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81b8f005d1f63613a05738d68e52e35c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7517f54a1ccb77add90ade02b3a84719.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
②求该公园的最大面积.
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2 . 下图的四个图象中,与下述三件事均不吻合的是( )
(1)我骑着车离开家后一路匀速行驶,只是在途中遇到一次交通堵塞,耽搁了一些时间;(2)我离开家不久,发现自己把作业本忘在家里了,于是返回家里找到了作业本再上学;(3)我从家出发后,心情轻松,一路缓缓加速行进.
(1)我骑着车离开家后一路匀速行驶,只是在途中遇到一次交通堵塞,耽搁了一些时间;(2)我离开家不久,发现自己把作业本忘在家里了,于是返回家里找到了作业本再上学;(3)我从家出发后,心情轻松,一路缓缓加速行进.
A.![]() | B.![]() |
C.![]() | D.![]() |
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解题方法
3 . 若
,
,
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3039f6d79e13e820f873657bd21f45d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f18672da192c8adfaf5b0d4e03a26d13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff43ee0759ded11ed553fb19e9cde4ae.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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名校
解题方法
4 . 定义在
上的函数
若满足:①对任意
,都有
;②对任意
,都有
,则称函数
是以
为中心的“中心捺函数”.已知函数
是以
为中心的“中心捺函数”,若
,则
的取值范围为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9f58d4591d668b4bc32fae4faab8298.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8f09c0670e752aa71b00f219f374b8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef357289121374304d64eeffac9517ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4562f3225c98cf5cb11b47d98c9cc9c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2c3dd8fa2dc8c0c7e255bfb054ad34c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7a999c36de5c9a9ce876a4a56fa34c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e922443dfc4a22cfb96bc051a2dd3f05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/586a00be943acb9327f3078db03591ae.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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|
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|
2卷引用:江苏省盐城市响水中学2023-2024学年高一上学期期中考试数学试题
解题方法
5 . 已知函数
的图象经过点
.
(1)求
的值;
(2)求函数
的定义域和值域.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12f7806c6ebbf84454a5b7d20e3b53df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6c7d1e7ffa7d5bfb2aa3c333536a8a9.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
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名校
解题方法
6 . 若函数
是
上的单调函数,则
的取值范围是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c639cb81e78e518f02d8fff319262561.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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|
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7 . 若函数
的定义域为
,则函数
的定义域为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa66623cf54b42d6d12be4c8edaa7071.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b76d89d9fb87bdc2a01a234afe1abced.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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|
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3卷引用:山东省名校考试联盟2023-2024学年高一上学期11月期中检测数学试题
山东省名校考试联盟2023-2024学年高一上学期11月期中检测数学试题(已下线)5.1 函数的概念与图象-【题型分类归纳】(苏教版2019必修第一册)湖北省新高考联考协作体2023-2024学年高一上学期12月联考数学试卷
8 . 吉祥物“冰墩墩”在北京
年冬奥会强势出圈,并衍生出很多不同品类的吉祥物手办.某企业承接了“冰墩墩”玩具手办的生产,已知生产此玩具手办的固定成本为
万元.每生产
万盒,需投入成本
万元,当产量小于或等于
万盒时
;当产量大于
万盒时
,若每盒玩具手办售价
元,通过市场分析,该企业生产的玩具手办可以全部销售完(利润=售价-成本,成本=固定成本+生产中投入成本)
(1)求“冰墩墩”玩具手办销售利润
(万元)关于产量
(万盒)的函数关系式;
(2)当产量为多少万盒时,该企业在生产中所获利润最大?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d01dd350dc95f42f1883e0cc7aae084.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90dd550e1ad9bbf01687ffb4aab788ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e6f1af4b44b2e97e8f319bab4ae9010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1789bfa58a3a97e0719e6997a2c332fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e6f1af4b44b2e97e8f319bab4ae9010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58bad9b6b29b972a7cd107592ab9074f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90dd550e1ad9bbf01687ffb4aab788ec.png)
(1)求“冰墩墩”玩具手办销售利润
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)当产量为多少万盒时,该企业在生产中所获利润最大?
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9 . 已知函数
满足对任意的
都有
,则实数
的取值范围为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9f7f86c41ef1da87a6a14d1ce243b3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fd423a80d5b6fea8753fa1813cfbcc4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8f09c0670e752aa71b00f219f374b8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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3卷引用:四川省成都市成都七中万达学校2023-2024学年高一上学期11月期中考试数学试题
解题方法
10 . 已知函数
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9249ce7e4ff523cfd1df9379be0efe2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e0079e132c74a4474a73c3636713eed.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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