Chapter 3 of 10All chapters
Chapter 3 of 10
Derivatives
Slope at a point.
What it tells you
The derivative is the slope of the curve at one point: how much the output changes for a tiny change in input. Positive means rising, negative falling, zero momentarily flat.
- Speed is the derivative of distance; acceleration is the derivative of speed.
- Marginal cost in economics is the derivative of total cost.
Reading a graph
You can sketch a derivative by eye: steep upward sections give large positive values, flat sections give zero, and peaks and troughs are where it crosses zero.