Polynomial Derivative Graph with Tangent and Slope Analysis

This GeoGebra example dynamically visualizes the derivative graph of a polynomial function, illustrating the geometric relationship between a function and its derivative. It demonstrates the core concepts of derivatives, tangents, roots, intersection points, and slope. Construction utilizes key GeoGebra commands including NDerivative, Tangent, Root, Intersect, and Slope, operating on function f, its derivative f', and points A, B, C, D. The model is suitable for high school and early college calculus courses, supporting intuitive teaching of derivative meaning, tangent line equations, function feature analysis, and the connection between algebraic expressions and graphical behavior.