Goal: See where the graph of a cubic function is concave, convex, increasing or decreasing. Adjust the coefficients of the polynomial to tailor the graph to your specifications.

A graphing window displays the graph of f(x) = ax³ + bx² + cx + d . Sliders at upper right control the values of a , b , c , and d . A slider below the window controls the value of x , a white disk marks the corresponding point on the graph, and a ghosted strut connects the slider position to the graph point (x,y) .

Violet disks mark extrema and blue cyan disks mark points of inflection.

Checkboxes select highlighting the portion of the graph having the following attributes: Rising (yellow), Falling (green), Concave (orange), Convex (red).

The expression for f(x) is displayed, as is the value of f(x) for the chosen value of x .

Rolling the cursor over the graphing window produces crosshairs and a readout of the values of x and y. Depressing the mousekey suppresses the crosshairs.

© 2010 H. Miller, H. Burgiel, and J.-M. Claus