Differentiation and Tangent to a Curve: Visualizing Slope Dynamics

① This GeoGebra example dynamically demonstrates the tangent line and its slope at a point on a function curve, visually illustrating the geometric meaning of the derivative—the tangent slope equals the derivative value at that point. ② Core mathematical concepts include derivatives, tangent lines, slope, and the rate of change of a function, rooted in fundamental calculus ideas. ③ Construction highlights: using GeoGebra's Tangent command to create the tangent line g to the curve f at point A, and the Slope command to compute the slope m of that tangent; points B and text objects text1 and text2 display the slope value and coordinates, allowing users to drag point A to observe how the tangent changes. ④ Suitable for high school or introductory college calculus students, this interactive tool helps grasp the definition of the derivative, tangent line equations, and local linear approximation, and serves as an effective classroom demonstration or self-study resource.