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Topic: A problem from our exams
Replies: 2   Last Post: Jun 6, 1997 7:40 PM

 Messages: [ Previous | Next ]
 Joshua Zucker Posts: 710 Registered: 12/4/04
A problem from our exams
Posted: Jun 4, 1997 2:22 PM

One of the chapter test questions we use in our course, toward the end
of calculus A, is:

5. Find the max and min of the function f(x) = 2/3 sin (pi*x) on the
interval [1,2]. Sketch its graph.

And then

6. Find the equation which x solves if x is the location of the
minimum value of g(x) = 1/x sin(pi*x) on the interval [1,2].
Is the minimum value larger or smaller than the minimum of f in the
previous problem? Hint: consider g(3/2) and g'(3/2).

#5 is a problem which can be done just fine by algebraic means. The
idea of doing it with a calculator seems absurd to me -- students
should be able to look at this function and immediately know what it
looks like. They shouldn't even need to do any algebra.

#6, then, is a problem that could be done with a graphing calculator.
But it seems to me that doing it without one builds more
understanding. Of course, if you wanted to find the ACTUAL minimum of
g, a calculator would be a fine way to go. But doing the algebra that
gives the equation the minimum would satisfy, and then seeing that the
minimum must be smaller because g(3/2) = f(3/2) = min of f, but
g'(3/2) is nonzero, seems much more revealing than just finding
something on the calculator.

questions? What is the role of the calculator (if any) in your opinion?

--Joshua

Date Subject Author
6/4/97 Joshua Zucker
6/5/97 LnMcmullin@aol.com
6/6/97 david klein