Date: Jun 29, 1995 3:06 PM
Author: Herbert Kasube
Subject: Analyzing Graphs with a Graphing Calculator

This question arose in an earlier post and I find it quite interesting.
I've been using graphing calculators in my calculus classes and have
found that my assessment procedures must change. My classroom discussions
are different, too.

For example, while discussing properties of the natural log function
recently I asked my students (In class) to use their calculators to graph
the two functions

f(x) = ln(x^2) and g(x) = 2 ln x

I made certain that they cleared the first function before graphing the
second. This led to a discussion of why the calculator gave two
"different" graphs even though many (most) of the students expected to
get the same graph. Questions like this utilize the power of the
technology without losing sight of some of the "pencil & paper" work needed.

Another example from an exam :

Use your graphing calculator to approximate the x-coordinate of
the relative minimum of the function

f(x) = x^5 - x^4 + x^2 - x

Merely zooming in on the point does not give very satisfactory results.
My suggestion with a similar example in class was to simultaneously graph
f'(x) and determine where its graph crosses the x-axis (going from
negative to positive) .

I feel that this type of example also combines the use of technology and
calculus analysis.

This is a VERY interesting thread that I hope we continue.

Herb Kasube
Department of Mathematics
Bradley University
Peoria, IL 61625