Introducing Derivatives via the Slope Function

① This example dynamically shows how the slope of a tangent line changes along a function's graph, visually introducing the derivative as a slope function. ② Core mathematical concepts include the geometric definition of the derivative, tangent slope, rate of change, and the relationship between a quadratic function and its derivative. ③ Construction highlights: using GeoGebra commands Point to place a movable point A on function f, Tangent to create the tangent line, Slope to compute its slope and plot the slope function g, and Segment with points S and h to visualize the slope value as a segment. ④ Suitable for high school or early college calculus students, this interactive tool helps bridge the gap from average to instantaneous rate of change and serves as an effective classroom demonstration for building intuitive understanding of derivatives.