David Little
Mathematics Department
Penn State University
Eberly College of Science
University Park, PA 16802
Office: 403 McAllister
Phone: (814) 865-3329
Fax: (814) 865-3735
e-mail:dlittle@psu.edu

The Derivative of a Function

The following applet can be used to approximate the derivative of f(x) by drawing the graph of the difference quotient for various values of h ≠ 0. Simply enter the function f(x) and the value h. The applet automatically draws the graph of f(x) and the corresponding difference quotient. As h approaches 0, the graph of the difference quotient will approximate the graph of the derivative of f(x). If you have a guess as to what the derivative of f(x) is, then enter this function as f'(x) and the applet will draw the graph of f'(x) (in gray) so that you can compare the two functions.

The value of h can be changed by simply typing a new value, such as "1.2345", "pi/2", "sqrt(5)+cos(3)", etc. The value of h is represented by a red dot on the x-axis. You can change the value of h by simply dragging this dot along the x-axis. To move the center of the graph, simply drag any point to a new location. To label the x-axis in radians (i.e. multiples of pi), click on the graph and press "control-r". To switch back, simply press "control-r" again.

Here is a list of functions that can be used with this applet.