Definition of Derivative: Secant Slope Approaching Tangent Slope

① This example dynamically demonstrates the core definition of the derivative: as point Q moves along the function curve toward point P, the slope of the secant line PQ approaches the slope of the tangent line at P, which is the derivative. ② It covers key calculus concepts including derivative, limit, secant line, tangent line, slope, and the fundamental idea of differential calculus. ③ Construction details: using GeoGebra commands such as Point, Line, OrthogonalLine, Intersect, Segment, Vector, and Midpoint, the construction includes the function f, moving points P and Q, secant line g, tangent line h₁, perpendicular lines, intersection points, vectors, and midpoints. A slider or draggable point controls Q's position, visually showing the transition from secant to tangent. ④ Suitable for senior high school or early university students learning calculus, this interactive tool helps build an intuitive understanding of the geometric meaning of the derivative, from average rate of change to instantaneous rate of change, and is also useful for classroom demonstrations.