In the episode "Bart The Genius" (7G02) of The Simpsons, fourth-grader Bart Simpson has cheated on a mathematics exam and pays for his evil ways by getting transferred to a school for gifted children, where he is way over his head.

   

   

Partial text translation of the scene:

Teacher:  So y = r cubed over 3. And if you determine the rate of change in this curve correctly, I think you'll be pleasantly surprised.
[The class laughs except for Bart who appears confused.]
Teacher:  Don't you get it, Bart? Derivative dy = 3 r squared dr over 3, or r squared dr, or r dr r.

Note that what the teacher says is not necessarily what she writes on the board!

1.  Explain in your own words what the calculus problem is that the teacher is solving. Explain each step of her written solution.  Is it correct?  If there is an error, explain and make the correction.  Is her verbal explanation completely correct?  If not, explain how you would change her wording.

2.  Explain the joke.  If English is not your first language, then you may wish to ask a native English speaker why this problem/solution is funny.  (I do not guarantee that it is hilarious.)

Dr. Andrew Nestler, Santa Monica College

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