Visualizing First and Second Derivatives

This interactive GeoGebra example visualizes the first and second derivatives of a function, allowing users to toggle graphs on or off to explore relationships between the original function, its tangent lines, and derivative curves. Core mathematical concepts include the definition of the derivative, slope of tangent lines, and how the second derivative indicates concavity. Construction uses the Derivative command to generate F' and F'', Point and Tangent commands to place points and draw tangents on the curves, Textfield and sliders (Xshift, Yshift, Xzoom, yZoom) for panning and zooming, and an input box (inputBoxF) to dynamically change the function. Suitable for high school and college calculus courses to deepen understanding of derivative geometry and function behavior.