Gradient of a Curve: Interactive Derivative and Tangent Demonstration

This GeoGebra applet introduces differentiation by interactively demonstrating the gradient of a curve. It shows how the slope of the tangent line at a moving point on a function graph represents the derivative, illustrating the geometric meaning of instantaneous rate of change. Core mathematical concepts include functions, tangent lines, slope, derivatives, and differential calculus. The construction uses GeoGebra commands Point, Tangent, Slope, and Distance, together with objects such as points A, B, lines l, m, m1, n, and text elements text1, text2 to display dynamic measurements and annotations. Designed for high school calculus beginners and undergraduate students, it supports classroom instruction and self-paced exploration of the graphical interpretation of derivatives.