IntroFoundations

Instantaneous Rate

Overview

What happens as the interval shrinks to zero? The average rate of change approaches the instantaneous rate — the derivative.

Key Concepts

1

Instantaneous rate = limit of the average rate as Δx → 0

2

Geometrically: the slope of the tangent line at a point

3

This is the central idea of differential calculus

See it in action

Use the interactive visualizer to explore this concept with real graphs.

Open Derivative Explorer