Gradient Function of a Parabola (Tangent Slope Demo)

① This example dynamically demonstrates how the slope of the tangent line to a parabola changes as a point moves along the curve, and simultaneously plots the corresponding gradient (derivative) function. ② Core mathematical concepts include quadratic functions, derivatives, tangent lines, and the relationship between a function and its derivative graph. ③ Construction highlights: using GeoGebra objects f (the parabola), a (a draggable point or parameter), and Tangent (the tangent command) to create the tangent line, then tracing the slope to generate the derivative curve. ④ Suitable for high school or early college students learning introductory calculus, ideal for classroom demonstrations or self-guided exploration of derivative concepts, and useful for teachers creating interactive materials.