Geometric Interpretation of Derivatives and Dynamic Tangent Slopes

This interactive GeoGebra example visually demonstrates the geometric meaning of the derivative as the slope of the tangent line to a function at a given point. It features a differentiable function f(x) with its derivative f'(x) computed via the Derivative command. Tangent lines are constructed at user-defined points A and B using the Tangent and Line commands, while the Slope tool dynamically displays the instantaneous rate of change. Interactive elements include InputBox objects for specifying x-coordinates (x_A, x_B) and Textfield components for explanatory labels. Built with objects such as sliders (a, b, c), auxiliary functions (g), and multiple text annotations, this construction supports inquiry-based learning in calculus. Ideal for high school advanced mathematics or introductory college calculus courses focusing on conceptual understanding of derivatives.