Observe the relationships between a function, its first derivative, and its second derivative. Use the coordinate readout to estimate the slopes of the graphs.

A pull down menu contains choices for a function \(f(x)\), whose graph is ghosted in a graphing window.

The value of \(x\) can be chosen by means of a slider under the window. The [>>] key initiates an animation, by smoothly increasing the value of \(x\). The [<<] key resets \(x\) to its minimal value.

The graph of \(f(x)\) is displayed in cyan. Checkboxes toggle display of graphs of \(f'(x)\) (in red) and \(f''(x)\) (in green) for values of \(x\) less than its chosen value. Further check boxes toggle display of the tangent line and of the approximating parabola.

A readout displays the current values of \(f(x)\), and of \(f'(x)\) and \(f''(x)\) if selected.

Rolling the mouse over the graphing window creates crosshairs and a readout of the values of \(x\) and \(y\). Depressing the mousekey suppresses this readout.

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