Gradient of y=x^3: Tangent Slope Visualization

This GeoGebra example visualizes the gradient (slope) of the tangent line to the cubic function y=x³ at any point, demonstrating the geometric interpretation of the derivative. It highlights core calculus concepts: derivative, tangent line, slope, and the limit process. Users can drag point P to see the secant line (g) approach the tangent line (h), with slope values m and m_1 updating dynamically. The construction uses commands Line, Tangent, and Slope, along with objects f, p, P, δx, Q, g, h, m, m_1, and auxiliary rectangles and special points. Ideal for high school or early college students learning differential calculus, and for teachers to illustrate how the derivative of x³ equals 3x². The interactive nature helps grasp the transition from secant to tangent and the concept of instantaneous rate of change.