Stage 36 · Limits, Derivatives & Their Applications
36.3.5 How Differentiability and Continuity Relate
36.3 What a Derivative Really Is: Concept and Geometry
Point 5 of 5
36.3.5 How Differentiability and Continuity Relate
Core ideaA curve with a sharp corner has no single tangent, so being differentiable always means being continuous, but being continuous doesn't guarantee differentiable.
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.