Stage 36 · Limits, Derivatives & Their Applications
36.2.4 Instant Rate of Change and the Birth of the Derivative
36.2 How Fast Things Change: From Average to Instant
Point 4 of 5
36.2.4 Instant Rate of Change and the Birth of the Derivative
Core ideaHow fast is it changing right now? It's the limit of Δy/Δx as Δx→0, written f′(x₀).
Module goal. Use a limit to squeeze "the average pace over a stretch" down into "the pace at this very instant," leading naturally to the heart of the derivative.