First and Second Derivatives of a Function

This GeoGebra example demonstrates the dynamic relationship between a function and its first and second derivatives by dragging a point along the graph of f. Core mathematical concepts include function graphs, first derivative, second derivative, geometric meaning of derivatives (tangent slope and concavity), and differential calculus. The construction uses GeoGebra commands Point to create a draggable point A on function f, Derivative to generate the first derivative g and second derivative h, and Textfield together with inputBox1 for function input; objects B, C, a, b and button1 support parameter linkage and annotation. It is suitable for high school calculus introduction and university mathematical analysis courses, ideal for visualizing derivative concepts and interactive classroom demonstration.