**How to Run the Mathlet**
The applet has two modes that are chosen from the dropdown menu located
at the top right corner of the applet: *Demo
examples* and *User defined function.*

In the *Demo examples mode* a graph
of a function f(x) is displayed in red in the grapher's window. You
are encouraged to sketch the graph of the derivative f '(x) in the same
window. Graphing can be done by dragging the mouse with the right mouse
button depressed. Your graph will appear in blue. You can erase the
sketch by clicking the ERASE button. The
real graph of the derivative f '(x) can be displayed by dragging
the blue button of the slider located below the graphing window.
As the slider is being dragged, a piece of the tangent line to the graph
of the function f(x) and the value of its slope are being dynamically
displayed to show the relationship between the slope of the tangent
line and the corresponding value of the derivative. The graph of the
derivative f '(x) will apear in green, and you can compare it with your
sketch. The button Next Example provides
a graph of a new function f(x). The examples are chosen to best illuminate
the geometric relationship between the graphs of f(x) and its derivative
f '(x).

The *User defined function mode*
allows you to enter a formula for a function f(x). A function f(x) is
entered in the input box to the right of the graphing window. The syntax
for doing so is the same as the syntax used by most graphing calculators.
All of the syntax rules, as well as a list of available functions, are
displayed by mousing over the button marked SYNTAX.
You can choose the x- and y-ranges in the graphing window by typing
them into the range boxes. After entering the data, click the GRAPH
button. The graph of f(x) will appear in the graphing window. Again,
you are encouraged to sketch the derivative f '(x). The actual derivative
f '(x) is displayed by dragging the slider with the mouse. The RESET
button clears the board and resets the ranges.

*© Copyright 2004 Barbara Kaskosz*