Drawing Derivatives: Interactive Exploration of Function and Its Derivative

This example uses a draggable red point B to let users attempt to manually sketch the derivative of a given curve, thereby intuitively grasping the geometric meaning of derivatives. Core mathematical concepts include derivatives, tangent slopes, the correspondence between a function graph and its derivative graph, and the dynamic visualization of a secant approaching a tangent using slope tools. The construction leverages GeoGebra commands: the Derivative command generates the derivative f' automatically, the Slope tool computes the tangent slope at a point, and Segment and Textfield display numerical values; buttons (button1, button2, button3) and an input box (InputBox2) control interactions, while sliders a and h adjust parameters, with list1 and point p assisting the drawing. Suitable for high school to early college students learning calculus, this example is ideal for classroom demonstrations or self-study, helping build an intuitive mapping from function graphs to derivative graphs and understand the essence of derivatives as instantaneous rates of change.