Cliff Diver Problem: Introduction to Derivatives

The 'Cliff Diver Problem' is a classic calculus visualization that dynamically demonstrates the geometric meaning of the derivative as the instantaneous rate of change along a parabolic trajectory. It models the path of a diver jumping from a cliff, mapping position over time. Core mathematical concepts include the derivative, trigonometric functions, function graphs, and the geometric interpretation of the tangent line slope as instantaneous velocity. To construct this, the GeoGebra script utilizes commands such as `Point`, `Line`, `Tangent`, `Intersect`, and `Slope` to define the trajectory function f, the tangent line L, and dynamically calculate slopes. LaTeX labels (text1, text2, etc.) are used to display real-time values. This resource is highly suitable for high school or introductory college calculus courses, helping students bridge the gap between algebraic formulas and geometric intuition.