Does Continuity Imply Differentiability?
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This GeoGebra example explores the fundamental relationship between continuity and differentiability in calculus. It demonstrates that continuity does not guarantee differentiability, using geometric constructions and function graphs to illustrate this key mathematical concept. The construction involves Point, Line, and various function-related objects (f, A, B, g, m1, etc.) to build visual representations. Suitable for high school and early university calculus students seeking to understand the distinction between continuous and differentiable functions.
GeoGebra Commands & Parameters
Point(f) → BPoint(h) → DPoint(i) → FLine(E, F) → kPoint(j) → HLine(G, H) → lLine(B, A) → mLine(D, C) → n
AI Drawing Prompt Reference
Draw a graph showing the difference between continuity and differentiability. Include a continuous but non-differentiable function curve, a differentiable function curve, and some auxiliary lines to distinguish them. The construction order starts with drawing the function curves, then adding auxiliary lines, and finally labeling key points to explain the difference.
The prompt above was compiled from the original drawing commands and is for reference only.