Definition of the Derivative: From Secant to Tangent

This GeoGebra example dynamically illustrates the definition of the derivative by showing how a secant line approaches the tangent line as two points on a function graph move closer together. It visually demonstrates the geometric meaning of the derivative as the instantaneous rate of change. Core mathematical concepts include derivative, tangent line, secant line, limit, and local linear approximation. Construction details: Points A and B are created on the function f, an orthogonal line is used to construct perpendiculars, intersections are found, a polygon is formed with the secant and axes, a text field and input box allow interactive input, and segments connect the points. By dragging point B toward A or using a slider, the secant slope is compared numerically with the derivative f'. This resource is suitable for high school or introductory college calculus students to grasp the limit concept behind derivatives, and serves as an interactive classroom demonstration or self-study tool.