Stage 36 · Limits, Derivatives & Their Applications
36.3.1 The Definition of the Derivative
36.3 What a Derivative Really Is: Concept and Geometry
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36.3.1 The Definition of the Derivative
Core ideaWrite the whole approaching process as one formula: f′(x₀)=lim[f(x₀+Δx)−f(x₀)]/Δx.
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.