23-24高二下·全国·课前预习
1 . 知识点三 函数图象的变化趋势与导数的绝对值的大小的关系
一般地,设函数
,在区间
上:
一般地,设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c7028a5fa4d781d382ca3b73b74796e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5296b39d62215c77a923ed5674b10b01.png)
导数的绝对值 | 函数值变化 | 函数的图象 |
越大 | 比较“ | |
越小 | 比较“ |
您最近一年使用:0次
23-24高二下·全国·课前预习
2 . 割线斜率与切线斜率
设函数
的图象如图所示,直线AB是过点
与点
的一条割线,此割线的斜率是![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85d193fe41eabf97168e5f5016324b7a.png)
________ .于是,当Δx→0时,割线AB的斜率无限趋近于过点A的切线AD的斜率k,即k=________ =
设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c2cec274d055a711936934698b13997.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/905ac6407cb466d2434da38a7c5bc058.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85d193fe41eabf97168e5f5016324b7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8c1639ce321a0e100bdc793f61df3c3.png)
您最近一年使用:0次
23-24高二下·全国·课前预习
3 . 知识点五 导函数的定义
从求函数
在
处导数的过程可以看出,当
时,
是一个唯一确定的数.这样,当x变化时,
就是x的函数,我们称它为
的________ (简称导数).
的导函数记作________ 或________ ,即![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9be1c518c1663eee81b4d13c8db456a.png)
.
从求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11abb76da45ffa52b47c3a6b9a03ac7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11abb76da45ffa52b47c3a6b9a03ac7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16515ca05229fe341868d8c23d9f2642.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d31f9ce464f2ce3b24833b70595941c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9be1c518c1663eee81b4d13c8db456a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4dcfdf0e8025c212c98808075d8afad.png)
您最近一年使用:0次
23-24高二下·全国·课前预习
4 . 知识点三 函数在某点处的导数
如果当Δx→0时,平均变化率
无限趋近于一个确定的值,即
有极限,则称
在
处可导,并把这个确定的值叫做
在
处的导数(也称为瞬时变化率),记作________ ,即
=![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6964df77cd765effefff5e6405c90098.png)
=![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6964df77cd765effefff5e6405c90098.png)
.
如果当Δx→0时,平均变化率
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7688109e1a422042e8ce925007582a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7688109e1a422042e8ce925007582a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c7028a5fa4d781d382ca3b73b74796e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a12609054bd6ea75c0ab3214bb2e0b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c7028a5fa4d781d382ca3b73b74796e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a12609054bd6ea75c0ab3214bb2e0b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16515ca05229fe341868d8c23d9f2642.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6964df77cd765effefff5e6405c90098.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7688109e1a422042e8ce925007582a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6964df77cd765effefff5e6405c90098.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/504633259a36f33bb8e323620998b675.png)
您最近一年使用:0次
23-24高二下·全国·课前预习
5 . 知识点一 瞬时速度
瞬时速度的定义
(1)物体在________ 的速度称为瞬时速度.
(2)一般地,设物体的运动规律是
,则物体在
到
这段时间内的平均速度为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cdb783174b72ceae5100dc051c4d925.png)
.如果
无限趋近于0时,
无限趋近于某个常数v,我们就说当
无限趋近于0时,
的________ 是v,这时v就是物体在时刻
时的瞬时速度,即瞬时速度![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8354e2efafc38e2f2e4f0f92dd89d618.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cdb783174b72ceae5100dc051c4d925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/793345c6e43ebc1e9e7037421d4dc9d8.png)
.
瞬时速度的定义
(1)物体在
(2)一般地,设物体的运动规律是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e418a26507298f6829feec0d07def04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d9fd58e71dcae6cafaf9037d20ebd76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f19c2d30ba888aa60e5b05534cf32014.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cdb783174b72ceae5100dc051c4d925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af222fdff32ce2bcb3992a60ef694a9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54ec106b92bc77e6716692a61a15a0d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9f58827347f7739452efeff88902307.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54ec106b92bc77e6716692a61a15a0d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9f58827347f7739452efeff88902307.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82120861c1c4f7cc1a7a3f169f082a81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8354e2efafc38e2f2e4f0f92dd89d618.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cdb783174b72ceae5100dc051c4d925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/793345c6e43ebc1e9e7037421d4dc9d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af222fdff32ce2bcb3992a60ef694a9f.png)
您最近一年使用:0次
名校
6 . 设函数
在
处存在导数为2,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11abb76da45ffa52b47c3a6b9a03ac7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e1c26506530d542b19da099407ad4be.png)
A.2 | B.1 | C.![]() | D.6 |
您最近一年使用:0次
2024-02-20更新
|
2736次组卷
|
8卷引用:6.1.1&6.1.2 函数的平均变化率、导数及其几何意义(4知识点+6题型+强化训练)-【帮课堂】2023-2024学年高二数学同步学与练(人教B版2019选择性必修第三册)
(已下线)6.1.1&6.1.2 函数的平均变化率、导数及其几何意义(4知识点+6题型+强化训练)-【帮课堂】2023-2024学年高二数学同步学与练(人教B版2019选择性必修第三册)云南省昭通市一中教研联盟2023-2024学年高二上学期期末质量检测数学试题(A卷)福建省福州市平潭县新世纪学校2023-2024学年高二下学期3月适应性练习数学试题(一)(已下线)第六章:导数章末重点题型复习(1)(已下线)模块五 专题3 全真能力模拟3四川省广安市华蓥中学2023-2024学年高二下学期3月月考数学试题广东省汕尾市陆河县河田中学2023-2024学年高二下学期4月第一次阶段测试数学试题(已下线)专题01 一元函数的导数及其应用-1
名校
7 . 若
上的可导函数
在
处满足
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e1a442cdf58724de628099973310555.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11abb76da45ffa52b47c3a6b9a03ac7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c835aaf8a072b1534d20897a3d0391d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e1a442cdf58724de628099973310555.png)
您最近一年使用:0次
2024-02-04更新
|
1581次组卷
|
6卷引用:6.1.1&6.1.2 函数的平均变化率、导数及其几何意义(4知识点+6题型+强化训练)-【帮课堂】2023-2024学年高二数学同步学与练(人教B版2019选择性必修第三册)
(已下线)6.1.1&6.1.2 函数的平均变化率、导数及其几何意义(4知识点+6题型+强化训练)-【帮课堂】2023-2024学年高二数学同步学与练(人教B版2019选择性必修第三册)湖北省武汉市华中师范大学第一附属中学2023-2024学年高二上学期期末检测数学试题(已下线)第二章 导数及其应用(基础检测卷)-2023-2024学年高二数学同步精品课堂(北师大版2019选择性必修第二册)(已下线)第六章:导数章末重点题型复习(1)贵州省贵阳市第一中学2023-2024学年高二下学期教学质量监测卷(三)数学试题(已下线)专题01 一元函数的导数及其应用-1
8 . 若函数在
处的导数等于
,则
的值为( ).
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2023-12-13更新
|
1192次组卷
|
5卷引用:第五章 一元函数的导数及其应用(知识归纳+题型突破)-2023-2024学年高二数学单元速记·巧练(人教A版2019选择性必修第二册)
(已下线)第五章 一元函数的导数及其应用(知识归纳+题型突破)-2023-2024学年高二数学单元速记·巧练(人教A版2019选择性必修第二册)上海市青浦区2024届高三上学期期终学业质量调研数学试题(已下线)6.1.1函数的平均变化率(分层练习,6大题型)-2023-2024学年高二数学同步精品课堂(人教B版2019选择性必修第三册)(已下线)2.2 导数的概念及其几何意义(分层练习)-2023-2024学年高二数学同步精品课堂(北师大版2019选择性必修第二册)(已下线)专题09 导数(三大类型题)15区新题速递
9 . 导数
(1)设函数
在区间
上有定义,
,若
无限趋近于0时,比值![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd6989eef65f4476379f1a16f30cf5b1.png)
_____ 无限趋近于一个常数
,则称
在
可导,并称该常数
为函数
在
处的____ ,记为
即
.
(2)
的几何意义就是曲线
在点_____ 处切线的_____ .
(3)若函数
在
内任意一点
可导,则
为
在
上的导函数.
(1)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4562f3225c98cf5cb11b47d98c9cc9c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee49cd415b686374189f90102d23ef7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1268e217016ff7e12b9bc51341c4cde.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd6989eef65f4476379f1a16f30cf5b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11abb76da45ffa52b47c3a6b9a03ac7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11abb76da45ffa52b47c3a6b9a03ac7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91421e7703d87617f50270178decd18a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e34817c02bca54629580be8e9ea60f2.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91421e7703d87617f50270178decd18a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/18/fdee788f-da21-4d31-bf59-34a35094aee1.png?resizew=227)
(3)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4562f3225c98cf5cb11b47d98c9cc9c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a4b04824a308519a61318a82aa97a05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4562f3225c98cf5cb11b47d98c9cc9c3.png)
您最近一年使用:0次
10 . 曲线上一点处的切线
(1)设
为曲线
上不同于
的一点,此时直线
称为曲线的____ ,随着点
沿曲线
向点
运动,割线
在点
处附近越来越接近曲线
,当点
无限逼近点
时,直线
最终成为在点
处最逼近曲线的直线
,这条直线称为曲线在点
处的_____ .
(2)设曲线上
,
,当
无限趋近于0时,割线
的斜率______ 无限趋近于点
处切线的_____ .
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5eefffa1689b5a68786b9a5875f12c0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/17/a7387044-3c3c-40c5-a84a-f850b113b736.png?resizew=218)
(2)设曲线上
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7775aa57ca0e62216f3039ed88dceed0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7e9db72d743d71cdee7f7d70cb17381.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1268e217016ff7e12b9bc51341c4cde.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7775aa57ca0e62216f3039ed88dceed0.png)
您最近一年使用:0次