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.

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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