Introducing the Derivative: Tangent Lines and Rate of Change

This GeoGebra example introduces the derivative by showing how a tangent line to a function graph changes as the point of tangency moves. It connects the geometric idea of a tangent line with the analytic concept of instantaneous rate of change, slope, and local linear approximation. The construction uses the function object f, a parameter a to control the point A on the curve, and the Tangent command to draw the tangent at A; objects b and c may support the tangent equation or auxiliary labels, while text1 provides explanatory text. It is suitable for high school calculus, introductory college calculus, or classroom demonstrations where students need to move from visual intuition to the formal definition of the derivative.