Geometric Meaning of the Derivative via Tangent Slope

This example demonstrates the geometric idea that the derivative is the slope of the tangent line at a given point on a function’s graph, turning the notion of instantaneous rate of change into an interpretable geometry problem. It centers on concepts such as derivative, tangent line slope, and the relationship between a function and a line determined by selected points or parameters. The construction (from the provided GeoGebra summary) uses Point to define key points (including those associated with f, A, and B), Line to create relevant straight lines (such as g and h), If to apply conditional logic for choosing or updating constructions depending on the configuration, and Slope to compute the slope values (m and m_1) of the lines. This makes it suitable for students learning calculus and function graph analysis in high school through the first year of college, especially for visual, interactive understanding of tangent lines and derivatives.