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Ruth Dover
Organization: Illinois Math and Science Academy
Department: Mathematics
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This notebook creates an animation that is designed to give a visual sense of the concavity of a function. The user inputs a function, a domain, and the number of frames to be shown. The graph is created. For each frame, segments of two tangent lines are drawn from nearby points and then a vertical segment is drawn to show the distance between these segments. This distance represents the change in the first derivative. These distances do not give actual approximations to the second derivative (due to the way in which they are created). Nevertheless, they are proportional so they give a relative sense of the size of the second derivative, and the user can see how the concavity changes as one moves along the graph. In the second graph, the second derivative is shown along with the vertical segment approximations (rescaled).

*Education > College
*Education > Precollege

concavity, second derivative
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ConcavityDemo.nb (14.8 KB) - Mathematica Notebook [for Mathematica 5.0]