Derivative Definition: Tangent vs Secant Lines Visualization

This interactive GeoGebra example illustrates the formal definition of a derivative by comparing the slopes of tangent and secant lines to a function. As the secant line’s two points converge, its slope approaches the tangent slope, embodying the limit process underlying differentiation. The construction employs GeoGebra objects such as a function f, a movable point P, a step size slider h, secant line s, tangent line t, and slope calculations, allowing students to explore the concept dynamically. Designed for high‑school and early university calculus courses, it supports visual and experimental learning of limits, rates of change, and the geometric meaning of derivatives.