Back to . . .

Curve Bank Home


NCB logo

NCB  Deposit #7

contributed by

Dr. Frank Wattenberg

United States Military Academy, West Point, NY


    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.


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.

Instructional illustration
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.

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

caution sign
Links to  the graphs in "Deposit #7" are

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.

NCB logo