Derivative of a Nonlinear Function: Curve, Tangent, and Segment Construction

This example visualizes the geometric meaning of the derivative for a nonlinear function by constructing a curve and its tangent, emphasizing how the slope of the tangent represents the local rate of change. It highlights core calculus ideas—derivatives as tangent-line slopes, the tangency condition between a function and a tangent, and the way key points and segments are determined by that construction. Construction in GeoGebra is driven by the commands Point, Tangent, and Segment: Point objects set up reference and tangency-related locations (objects include f, A, g, B, h), Tangent creates the tangent line at the chosen location on the curve, and Segment draws the connecting/measure lines that link the tangent construction to the selected points. Suitable for high-school advanced learners and first-year undergraduates studying calculus, function graphs, and tangent-line interpretation.