This mathlet provides an interactive and visually engaging way for students to explore the geometric relationship between the graph of a function and the graph of its derivative. The mathlet may help students to develop a sense of the shape of the graph of the derivative, given the graph of a function. It also gives students an opportunity to practice graphing derivatives on their own.
Barbara Kaskosz is a Professor of Mathematics at the University of Rhode Island.
In its Demo Examples mode, the mathlet displays a variety of examples of graphs of functions f(x). The user is encouraged to sketch with the mouse the graph of the derivative f '(x) in the same window. The real graph of the derivative f '(x) can then be displayed by dragging a slider, so students can evaluate their own graphs. 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 displayed dynamically to show the relationship between the slope of the tangent line and the corresponding value of the derivative.
The User Defined Function mode allows the user to enter a formula for a function f(x) in simple syntax, basically the same as that used by most graphing calculators. The user can choose the x- and y-ranges as well. After entering the data and clicking a button, the graph of f(x) appears. Again, the user is encouraged to sketch the derivative f '(x), and the actual derivative f '(x) is displayed by dragging the slider.
Open Derivative Plotter in a new window
For classroom demonstrations with a computer projector
For discussions with students in smaller groups in a laboratory setting
For independent exploration by students
The mathlet will run on any machine with a generic browser as long as it has Flash Player 6 or higher. The free and small (668KB) Player can be easily downloaded and installed from the Macromedia site -- click on the button at the right. Netscape 6 or higher usually comes with the Player ready to use.
Published September, 2004
© Copyright 2004 by Barbara Kaskosz