Derivative as a Function: Dynamic Tangent Slope Graphing

This GeoGebra example demonstrates how the slope of the tangent line to a curve is displayed and traced on a secondary graph as a point moves along the original function, thereby visualizing the derivative as a function. It explores several common functions, illustrating the correspondence between a function and its derivative. Core mathematical concepts include the derivative as a function, tangent slope, instantaneous rate of change, and the graphical relationship between f and f′. Construction relies on GeoGebra commands such as Element, Point, Vector, Textfield, Tangent, Slope, and Locus, with objects including function list flist, individual functions f_1 through f_13, points A, B, C, D, E, F, G, O, H, input elements button1 and inputBox1, and dynamic text labels. Suitable for high school calculus and introductory university calculus courses, ideal for classroom demonstration and student inquiry into the geometric meaning of derivatives.