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

Graphing the Derivative of a Function

The following applet can be used to draw a graph of the derivative of f(x). Simply enter the function f(x) and the point of tangency, a. The applet automatically draws the graph of f(x) (in black) and the line tangent to f(x) at x=a. The slope of the tangent line is displayed in the lower left corner of the screen and plotted on the graph (red dot).

As you move the point of tangency (green dot), the applet plots the slope of each tangent line, thereby drawing a graph of the derivative of f(x) (in red). 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 graphs.

The value of a can be changed by simply typing a new value, such as "1.2345", "pi/2", "sqrt(5)+cos(3)", etc. You may also change this value by using the up/down arrow keys. 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.