Maths 4.1Free videoLesson 1 of 9 in Module 4
Derivatives: Rate of Change and the Tangent
Say what a derivative measures, and read its sign and size off a graph.
Watch the lesson: Derivatives: Rate of Change and the Tangent
In this lesson10 parts
- 01Which way is down?
- 02Rate of change between two points
- 03Letting the gap shrink
- 04The derivative as a function
- 05Reading the sign and the size
- 06Checkpoint: the derivative so far
- 07The hero cars' error against the slope
- 08When a smaller h is worse
- 09Derivatives in Python
- 10Recap, challenge, and next: derivative rules
Key terms: Derivatives: Rate of Change and the Tangent
The words this lesson introduces, each in one line. The module’s glossary collects them all, and the AI glossary has every term across the courses.
- rate of change
Δy/Δx, the change in the output per unit change in the input |x²from 1 to 2:3- secant
- a line through two points of a curve | through
(1, 1)and(2, 4), slope3 - limit
- the value a quantity approaches as
hgoes to zero |2 + h → 2 - tangent
- the line that touches the curve at a point with the curve's slope there |
y = 2x − 1atx = 1 - derivative
- the slope of the tangent, the limit of
Δy/Δx|2forx²at 1 f′(x)- the derivative of
f, a function ofx|x² → 2x dy/dx- the same derivative, written as a ratio of small changes |
d(x²)/dx = 2x
Quiz: Derivatives: Rate of Change and the Tangent
Your first pick on each question is the one that counts. Getting one wrong here is how the lesson sticks.