Rate of Change with Limits: Visualizing Tangent Slope and Derivative

① This example dynamically shows how a secant line approaches a tangent line as a point moves closer to another on a curve, illustrating the concept of instantaneous rate of change (derivative) via limits. ② Core mathematical concepts include limits, rate of change, tangent slope, derivative, and linear approximation, with geometric interpretations of secant and tangent lines. ③ Construction highlights: using GeoGebra commands such as Point, Line, Tangent, Slope, Intersect, and OrthogonalLine, the curve f is built with movable points A and B; the secant line g and tangent line h are generated, and the slopes m (secant) and m_1 (tangent) are displayed numerically, with text1 explaining the limiting process. ④ Suitable for senior high school or introductory college calculus students, this interactive tool helps grasp the geometric meaning of the derivative and can be used for classroom demonstrations or self-study.