Demonstration of Differentiability

This example illustrates the geometric meaning of a function's derivative and tangent line at a specific point by dynamically moving point P along the function f. Observing the changes in tangent line L and its slope m demonstrates the concept of derivatives as limits. Core math concepts include functions, derivatives, tangent lines, and limits. GeoGebra commands like Point, Tangent, f, f', P, Q, L, m, text1 are used to dynamically construct the tangent line and visualize the derivative. Suitable for calculus beginners or high school math competition participants to understand derivative definitions and geometric applications.