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Discussion: Traffic Jam Applet tool
Topic: "Graphing Calculator" Software
Related Item: http://mathforum.org/mathtools/tool/10/


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Subject:   The exponential function
Author: Gene
Date: Sep 19 2003
I first showed them several exponential functions using Graphing Calculator
(2^x, 3^x, etc.), then used the Derivative and Tangent Line applet on the same
functions. They surmised that the derivative of an exponential function should
be an exponential function. We manipulated the definition of derivative to see
that the derivative of a^x is of the form ca^x, where c is the derivative at
0.

They agreed it would be nice to have a number for which the c turned out to be
one, and by trying various numbers like 2.7.2.71, 2.718 in Derivative and
Tangent Line Applet (and zooming), we got a number "a" for which the derivative
of a^x was pretty close to itself. By then almost everybody was recognizing
e.

This worked well but there may be applets that do it cleaner. Know any?

I passed back the quiz I gave last meeting. Some folks had problems figuring out
the shapes of derivative curves, as in the Derivative Puzzle applets, and I
recommended they go play with these till they can do them. I promised to put
similar problems on midterm and/or final and expect most who need it will
actually do it.


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