Stage 36 · Limits, Derivatives & Their Applications

36.3.2 The Slope of the Tangent Line

36.3 What a Derivative Really Is: Concept and Geometry

Point 2 of 5

36.3.2 The Slope of the Tangent Line

Core idea

Zoom in on the curve until it looks like a straight line, and the steepness of that little piece is f′(x₀).

Module goal. Promote the derivative from "a number at one point" to "a brand-new function," and nail down its geometric meaning once and for all: the slope of the tangent.
eastmath.com · 36.3 What a Derivative Really Is: Concept and Geometry · 36.3.2 The Slope of the Tangent Line