I answered a nice question on WyzAnt about approximating roots to a quadratic equation that had real but irrational roots.
Calculus enables us to find rational approximations to these irrational roots. I will re-present the solution to the problem, and continue to find a general expression to do this for an arbitrary polynomial.
"Problem: approximate...
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For http://www.wyzant.com/resources/answers/30521/12x_3_65x_2_24x_10_0

MP3 players example
The profit in millions of dollars for an MP3 player can be done with the polynomial P=-4x^3 + 12X^2 + 16X. X represents the number of MP3 players produced annually. The company currently produces 3 million MP3 players and makes a profit of $ 48,000,000. To figure out the least amount of MP3 players the company can produce and still make the same profit...
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