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