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 \(f(x) = ax^3 + bx^2 + cx + d\). 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