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

hkasube@bradley.bradley.edu