Estimating the Graph of the Derivative Function

This example shows how to estimate the graph of the derivative function f′ for a given function f using numerical methods. Users can input a function expression and use interactive input boxes and sliders to select interval endpoints A and B, then compute the slope of the secant line to approximate the instantaneous rate of change (derivative) at various points. The core mathematical concepts include the definition of a derivative, the relationship between secant and tangent lines, the idea of limits, and the geometric meaning of the derivative function. The GeoGebra construction employs Textfield, Segment commands and objects such as f, f′, A, B, etc., to draw secant lines and dynamically update slope displays. Learners can observe how the original function’s graph corresponds to its derivative’s graph, deepening their understanding of fundamental calculus concepts. This example is suitable for high‑school or first‑year university calculus courses and serves as an interactive tool for exploring derivative graphs.