Instantaneous Rate of Change
Core Sentence / 核心句
Instantaneous rate of change is the limiting value of average rates of change at a point.
中文理解：瞬时变化率是一段平均变化率缩到某一点后的极限。
Formula / 公式或规则
When To Use / 什么时候用
看到 at an instant、at a point、derivative as rate，就想到 instantaneous rate of change。
Watch Out / 易错点
如果 derivative 不是 simple rate of change，就把它理解成 local linear change 会更稳。
Search and Source Mentions / 搜索与出现位置
Mentioned In / 出现位置
- 02 - The Paradox of the Derivative · Knowledge Point 1: Instantaneous Rate of Change Is a Paradox
Knowledge Point 1: Instantaneous Rate of Change Is a Paradox
- 02 - The Paradox of the Derivative · 1. The derivative measures an instantaneous rate of change.
1. The derivative measures an instantaneous rate of change.
- 02 - The Paradox of the Derivative · 3. Instantaneous rate of change is the limit of average rates of change.
3. Instantaneous rate of change is the limit of average rates of change.
- 02 - The Paradox of the Derivative · Knowledge Point 6: Secant Line Becomes Tangent Line
instantaneous rate of change -> tangent slope
- 02 - The Paradox of the Derivative · 1. What This Episode Is About / 这一集在讲什么
The goal is to explain what a derivative is, and why the phrase "instantaneous rate of change" is subtle.
- 02 - The Paradox of the Derivative · 6. Visual Intuition Map / 图像直觉图
instantaneous rate of change
- 02 - The Paradox of the Derivative · 8. Confusion / Questions
1. 为什么 “instantaneous rate of change” 是矛盾说法？
- 02 - The Paradox of the Derivative · 3. Class Flow / 视频脉络
1. 提出问题：导数常被叫做 **instantaneous rate of change**，但这个说法有悖论