Derivatives of Polynomial Functions: Tangent and Slope Visualization

① This GeoGebra example dynamically illustrates the tangent line and its slope at a movable point on a polynomial function, making the geometric meaning of the derivative as an instantaneous rate of change visually intuitive. ② Core mathematical concepts include polynomial functions, derivatives, tangent slopes, and intersections of function graphs, with extensions to exponential functions, geometric mean, and correlation. ③ Construction highlights: using the Tangent command to create the tangent line g to the function f at point A, the Slope command to compute the slope m of the tangent, and a point B to track the slope value; dragging point A reveals how the tangent and slope change along the curve. ④ Suitable for high school to early college calculus courses, ideal for classroom demonstrations or student self-exploration to grasp the relationship between derivatives and local behavior of functions.