1 . 设函数
,其中
,已知
,且
.
(1)求
的解析式;
(2)求
的单调递增区间;
(3)将
的图象向左平移
个单位长度后,得到函数
的图象,若存在
,使得
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/766fea62d09b42af8b11244a70485174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40be0cfe807b44c2b0097fdd3920cffb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06f5aea3655b47e34a582dc600ff61d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5518ac9acc1de1b1005188d23c8bb6d.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
(3)将
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/037fb348109dc2063a268b10eb925a57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/028517e8bebe634441e0a5c79828e88a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e8afa701e97a54dd557f634e9a57f78.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7d84f2f62a7f41113c6d8e55dc99fcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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2 . 如图、某港口O要将一件重要物品用小艇送到一艘正在航行的轮船上,在小艇出发时,轮船位于港口O北偏西
方向且与该港口相距
的A处,并以
的航行速度沿正东方向匀速行驶,假设该小艇沿直线方向以
的航行速度匀速行驶,经过
与轮船相遇.(假设水面平静)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/6/19/6b7939b6-56a3-4ae7-90d0-7b6d0d796451.png?resizew=168)
(1)要使相遇时小艇的航行距离最短,小艇的航行速度应为多少?
(2)假设小艇的速度最快只能达到
,要使小艇最快与轮船相遇,应向哪个方向航行?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6b86c22b670a8e9f3896f9e8883fbbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7d1525355976915a23b0a3050e6a687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdde1bd791be76f4dfc0116f5c8dacce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6737e5a65b0067db9bdac02a52de7131.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3ee630252dc9ec9c8453d1561a81743.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/6/19/6b7939b6-56a3-4ae7-90d0-7b6d0d796451.png?resizew=168)
(1)要使相遇时小艇的航行距离最短,小艇的航行速度应为多少?
(2)假设小艇的速度最快只能达到
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d568215783a27afd4041395551623c4a.png)
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名校
3 . 设函数
的导函数为
的导函数为
的导函数为
.若
,且
,则
为曲线
的拐点.
(1)判断曲线
是否有拐点,并说明理由;
(2)已知函数
,若
为曲线
的一个拐点,求
的单调区间与极值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2a00a7220fe1f1699aa32ea0c70a303.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2183b5237f02670ccbe463aaaca37977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca0b72923071c1010a36f17cb3d1168b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca411f2905fd482bd14cb0092e5a6279.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ea9154699908e7a530d9e04830c9315.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43db00e106c7d08a76a7ba71ca5e63d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
(1)判断曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c683786f6c924632d9ca47ea243700e7.png)
(2)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/341534f0072c55c40cc00ed25097c2fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9bfaad7a770a2bb3930de1ed7444d90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
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5卷引用:辽宁省沈阳市第二中学2024届高三下学期三模数学试题
(已下线)辽宁省沈阳市第二中学2024届高三下学期三模数学试题河南省部分重点高中2023-2024学年高三下学期5月联考数学试卷 (新高考)2024届青海省海南藏族自治州高考二模数学(理科)试卷内蒙古自治区锡林郭勒盟2024届高三下学期5月模拟考试理科数学试题(已下线)拔高点突破05 函数与导数背景下的新定义压轴解答题(九大题型)
名校
解题方法
4 . 定义两个向量组
,
的运算
,设
,
,
为单位向量,向量组
,
分别为
,
,
的一个排列,则
的最小值为____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/858abf937bceeabf58fa26f5e2ffa418.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cbea56fd5adb7789d6aa1de90b65286.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/277a03c880a98dd28733c3ce21487b9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0411792b587ddd3e04440392f011c224.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b95d660852c5226ff65a21cfb36b8b39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17ccfda9afde4441cfd1d4df5fe9622d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/858abf937bceeabf58fa26f5e2ffa418.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cbea56fd5adb7789d6aa1de90b65286.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0411792b587ddd3e04440392f011c224.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b95d660852c5226ff65a21cfb36b8b39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17ccfda9afde4441cfd1d4df5fe9622d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebcc9443a8230fb9f3726fc7cb6b3521.png)
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名校
解题方法
5 . 已知函数
及其导函数
的定义域均为
,若
是奇函数,满足
,且对任意
,
,
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
![](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/01a4717b971daeae2bf1f9370c9ce8c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f370a1d4dd341e5ab1774a66c66c1204.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89867b421750df2435356f115bfd8c29.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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6 . 已知a,
,若
,
,则b的可能值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dd0914dc4d4c7f75710ff460a286fcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07de49f290b3fd36733d129379d19c8d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efdc0e0ca559f0f1af6127545f356fa2.png)
A.2.5 | B.3.5 | C.4.5 | D.6 |
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7 . 在
中,若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41de4d71f031a145ffee28a1c487baed.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/854e68b995b672792bb915ef502fcd5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41de4d71f031a145ffee28a1c487baed.png)
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名校
解题方法
8 . 某工厂有甲、乙两个生产车间,其污水瞬时排放量
(单位:
)关于时间
(单位:
)的关系均近似地满足函数
,其图象如图所示.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/6/23/26d08519-def2-4de0-a24a-c37a31e041f7.png?resizew=162)
(1)根据图象求函数解析式;
(2)若甲车间先投产,1小时后乙车间再投产,求该厂两个车间都投产
时刻的污水瞬时排放量;
(3)由于受工厂污水处理能力的影响,环保部门要求该厂的两个车间任意时刻的污水排放量之和不超过
,若甲车间先投产,为满足环保要求,乙车间比甲车间至少需推迟多少小时投产?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1ff4266515b801477248b32e10f3ac4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f42a97e3ae09c48e1d587f59af3621bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/795ea8d61f4e4e138231819356f4073b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/6/23/26d08519-def2-4de0-a24a-c37a31e041f7.png?resizew=162)
(1)根据图象求函数解析式;
(2)若甲车间先投产,1小时后乙车间再投产,求该厂两个车间都投产
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16dca1f69db5d45d7e0195b60f546a40.png)
(3)由于受工厂污水处理能力的影响,环保部门要求该厂的两个车间任意时刻的污水排放量之和不超过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d18b1b3fa4bc1f8e48a68b9f77e37e3b.png)
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解题方法
9 . 在锐角三角形
中,
,若
,则
的取值范围是_________________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6abef9318cce9afa6638a2c936e1b111.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e258ab9e600435b37465092243d99f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d2935ab6c068e0c7b4e07633388d254.png)
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解题方法
10 . 下列说法正确的是( )
A.已知复数![]() ![]() ![]() ![]() ![]() |
B.已知![]() ![]() ![]() |
C.有两个面互相平行,其余各面都是平行四边形的多面体是棱柱 |
D.![]() |
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