Limits, Rates of Change, and Tangent Lines

This GeoGebra example dynamically illustrates the relationship between limits, average rates of change, and tangent lines. It shows a function curve with a fixed point A and a moving point B; as B approaches A along the curve, the secant line through A and B gradually becomes the tangent line at A, revealing the geometric meaning of the derivative. Core mathematical concepts include limits, difference quotients (rates of change), and the definition of a tangent line. The construction uses the Intersect command to find intersection points, Point to create dynamic points, and Line to draw the secant line, with a slider h controlling the horizontal distance between A and B to animate the transition. This is suitable for high school or introductory college calculus students to grasp the intuitive foundation of derivatives, and also serves as an effective classroom demonstration tool.