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