Game: Sketching Curves Using Derivatives and Concavity

This interactive game focuses on sketching function curves by analyzing derivatives and concavity. It demonstrates how the signs of the first derivative (f') and second derivative (f'') determine the monotonicity, extrema, and concavity (including inflection points) of the original function f. Core mathematical concepts include derivatives, second derivatives, increasing/decreasing intervals, local extrema, concavity, and points of inflection. The construction uses GeoGebra commands such as Point to place key points (A, B, C, D, E) and FitPoly to fit a polynomial through them, while also plotting f, f', and f'' with a slider a for dynamic parameter adjustment. Suitable for high school or early college calculus students to reinforce the connection between derivative information and graph shape, and can be used as a classroom activity or self-paced practice game.