Cubic Derivative Trace

This example demonstrates the relationship between a cubic function and its derivative by dynamically tracing the tangent points and slopes. It visually illustrates the geometric meaning of the derivative in relation to the original function's graph. Key mathematical concepts include derivatives, function graphs, tangent slopes, and geometric transformations. The construction uses GeoGebra commands like Point, Tangent, and Slope, along with objects such as f (function), A (tangent point), g (derivative function), m (slope), B, m_1, m_2, and C. It is suitable for high school calculus instruction to understand the geometric significance of derivatives and local properties of function graphs.