Tangent, First and Second Derivatives of a Cubic Function

This GeoGebra example demonstrates a cubic function together with its tangent line, first derivative, and second derivative. It highlights the geometric meaning of derivatives: the slope of the tangent at a moving point, the relationship between f and f', and how f'' describes concavity and inflection behavior. The construction uses Point and Tangent to create a point on the curve and its tangent, Slope to display the tangent slope, Derivative to generate f' and f2, and Root, Intersect, and OrthogonalLine to locate zeros, intersections, and auxiliary lines. It is suitable for high-school calculus, introductory derivative lessons, and interactive function-graphing activities.