Problem of the Week: Another Nice Calculus Exam

By Department of Mathematics

Editor’s Note: The Department of Mathematics at Gettysburg College hosts a problem of the week challenge to determine each semester’s Paul Mugabi problem-solving award recipient(s). Each week’s entries are scored by a panel of faculty judges, and winner(s) from each week will receive a Problem Of the Week (P.O.W.) button.  The Gettysburgian is not involved in or responsible for accepting or evaluating students’ submissions to this contest.

THE RULES:

The contest is open to all Gettysburg College students. Up to three people may work together on a submission. Make sure your name is on your submission and that any sources are properly cited! Send solutions to bkennedy@gettysburg.edu or put solutions in the marked envelope in the hallway outside Glatfelter 215. This problem was posted on Friday, April 5 and solutions are due on Friday, April 12 by 5:00 p.m.

THE PROBLEM:

I took a calculus exam where I was confused about the chain rule: I thought that (f ◦g)'(x) = f'(x)g'(f(x)).

Nevertheless, when my professor gave me two functions f(x) and g(x) and asked me to find (f ◦g)'(x), I got it right!

Assuming that f(x) = x^3, find some possibilities for what the function g(x) is — try to find a lot of them!

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Author: Gettysburgian Staff

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