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. Check boxes 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, Heidi Burgiel, and J.-M. Claus