Does Differentiability Imply Continuity?

This GeoGebra example demonstrates the geometric relationship between differentiability and continuity at a point on a function graph, visually addressing the fundamental calculus question “Does differentiability imply continuity?” Core mathematical concepts covered include differentiability, continuity, limits, derivatives, and function graphing. The construction relies on GeoGebra commands Point and Line to create points A, B, B₁, C, D, E and lines a, b, c, g, h, i, j, k, together with the function object f and text label text1. By observing the dynamic positional relationships among points and lines, learners can see how the existence of the derivative limit forces the function value to be continuous. Suitable for high school elective courses and introductory university calculus, this example supports teacher-led concept clarification and independent student exploration of the logical implication between differentiability and continuity.