Click on the graph of the original function

Click on the graph of the first derivative

Click on the graph of the second derivative

About First and Second Derivatives

The graph of a function \(f(x)\) is closely related to the graphs of its first and second derivatives: Using these clues, it is possible to determine which of the graphs in this applet is the original function, which is its first derivative, and which is its second derivative.

Using the Applet

The applet will generate three graphs, representing the functions \(f(x)\), \(f'(x)\), and \(f''(x)\). The function \(f(x)\) will be a polynomial (that is randomly generated using a selection of points within the graphing window and Lagrange interpolation). By studying the three graphs and the properties above, decide which of the three graphs is the actual function \(f(x)\), and click on it. You'll then be asked to decide which of the two remaining graphs is \(f'(x)\).

About this Applet

This applet was created using JavaScript and the Raphael library. If you are unable to see the applet, make sure you have JavaScript enabled in your browser. This applet may not be supported by older browsers.