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

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Joshua Zucker

Posts: 710
Registered: 12/4/04
A problem from our exams
Posted: Jun 4, 1997 2:22 PM
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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.

What do you think about this kind of problem? Are these good test
questions? What is the role of the calculator (if any) in your opinion?


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