Graph of a Function and Its Derivative

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NCB Deposit #7

contributed by

Dr. Frank Wattenberg

United States Military Academy, West Point, NY

from http://www.joma.org/vol2/articles/wattenberg/contents.html

Sylvanus Thayer
"Father of West Point"

First, consider the function: equations

Spend some moments investigating how to move the arrows, "Mark points" and "Clear marked points" on the light blue grid at the left.

Then consider the green grid on the right.
The red curve is the graph of the functionand the blue curve is the graph of its derivative.

equation

On the left blue grid, the original parameters were a = 0 and b = 0.
Moving the points about the surface changes the values of aand b.

By only changing "a" in this graph,the derivative retains a value of ( 0, 0 ).

This is another way of saying that changes in "a" do not move the derivative from the origin.

[Note: In translation of functions, the vertical motion correlates to the sign of the constant term.]

Depost # 7 Links

Wattenberg has instructions for writing "Lite Applets" to create interactive web sites. See the following links.

http://www.joma.org/vol2/articles/wattenberg/parameter_plane.html

http://www.joma.org/vol2/articles/wattenberg/image_and_cursor.html

http://www.joma.org/vol2/articles/wattenberg/JOMA_article/wattenberg1.html

http://www.joma.org/vol2/articles/wattenberg/JOMA_article/wattenberg2.html

Frank Wattenberg is a Professor in the Department of Mathematical Sciences at the United States Military Academy, West Point.

Links to the graphs in "Deposit #7" are
http://www.dean.usma.edu/math/people/wattenberg/Lite_Applets/Parameter_Plane/cusp.html
or
http://www.joma.org/vol2/articles/wattenberg/Parameter_Plane/cusp.html

This particular Applet may not work on a MAC using Netscape 6 or 7. The Applet functions nicely on MACs running Internet Explorer. These Applets seem to work correctly on a PC running all newer browsers. Java code does not seem to be compatible in all platforms.