Dr. Nestler - Math 7 - Calculus 1 - Derivative Applications

Exercise 1.  In the episode “Homer Defined” (8F04) of The Simpsons, Homer reads a copy of the "US of A Today" newspaper.

Homer: Here's good news!  According to this eye-catching article, SAT scores are declining at a slower rate!
Lisa:  Dad, I think this paper is a flimsy hodgepodge of pie graphs, factoids and Larry King.
Homer:  Hey, this is the only paper in America that's not afraid to tell the truth, that everything is just fine.

Describe and sketch the shape of the graph of SAT scores over time, using Homer’s description.  You should mention derivatives in your explanation.

Exercise 2.  The slogan of the Lowe’s Home Improvement company is “Improving Home Improvement.”

Assuming that this is what the company really does, explain how there is a second derivative at work in this slogan.  First, define or explain what is meant by home improvement.  Next, identify a relevant function and variable (obviously you will not give a formula), and then analyze what the first two derivatives (and their signs) mean.

Possible hints:  First, try to find a first derivative of a function in the slogan.  A complete correct response to this exercise could consist of just a few sentences.

Exercise 3.  The following quote by mathematician Hugo Rossi appeared in the article, “Mathematics is an Edifice, Not a Toolbox” in Notices of the American Mathematical Society, Vol. 43, No. 10, Oct. 1996:

"In the fall of 1972 President Nixon announced that the rate of increase of inflation was decreasing. This was the first time a sitting president used the third derivative to advance his case for reelection."

Explain Rossi’s analysis of Nixon’s statement, by identifying a relevant function and variable (a formula is not required), and explaining Nixon’s use of a third derivative.

Dr. Andrew Nestler, Santa Monica College

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