解题方法
1 . (多选)如图,弹簧挂着的小球做上下运动,它在ts时相对于平衡位置的高度h(单位:
)由关系式
确定,其中
小球从最高点出发,经过
后,第一次到达最低点,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb2f95b382b3711c5ab2187b7f2c5c0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa92ac8b6521ff904cfa5939a3e6061a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cae27d0ed5b60ec23b51470dddbace5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdbb40016e1c6ea147a63ab384034336.png)
A.![]() |
B.![]() |
C.![]() |
D.![]() |
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23-24高二下·全国·课前预习
2 . 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“ |
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23-24高二下·全国·课前预习
3 . 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)
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23-24高二下·全国·课前预习
4 . 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)
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23-24高二下·全国·课前预习
5 . 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)
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23-24高二下·全国·课前预习
6 . 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)
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7 . 已知
的值是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/582a4e17a4fa67281e5e1c3a5d9d6aec.png)
A.1 | B.2 | C.![]() | D.![]() |
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8 . 设函数
的导函数为
,若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a875a4f0d860d3a2731c8914cd6f4ad8.png)
______ .
![](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/2a14beb86259d6bb43acfb1f176ce0c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a875a4f0d860d3a2731c8914cd6f4ad8.png)
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2024-03-27更新
|
408次组卷
|
3卷引用:上海市建平中学2023-2024学年高二下学期3月质量监测数学试卷
23-24高二下·全国·课前预习
9 . 判断正误,正确的写正确,错误的写正确.
(1)在平均变化率中,函数值的增量为正值.( )
(2)瞬时变化率是刻画某函数值在区间
上变化快慢的物理量.( )
(3)函数
在
处的导数值与
的正、负无关.( )
(4)![](https://staticzujuan.xkw.com/quesimg/Upload/formula/136eecfa8b1e39f9e7bb39168900b017.png)
.( )
(1)在平均变化率中,函数值的增量为正值.
(2)瞬时变化率是刻画某函数值在区间
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/351629c193354cdcf202133052e45028.png)
(3)函数
![](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/d1268e217016ff7e12b9bc51341c4cde.png)
(4)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/136eecfa8b1e39f9e7bb39168900b017.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9f6234ccd85f2357ec3b1427e54d36b.png)
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10 . 若函数
,
(1)用定义求
;
(2)求其图象在与
轴交点处的切线方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0519192532883d560482ad071e7b54c4.png)
(1)用定义求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
(2)求其图象在与
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
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