Difference between revisions of "2005 iTest Problems/Problem 6"
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Latest revision as of 19:08, 13 October 2025
Problem
Kathryn, for a history project on sports, chronicled the history of college football. When she mentioned that Auburn got cheated out of the NCAA Football championship in the 
season due to the many flaws in the BCS system, her teacher just couldn’t contain her applause, and awarded an automatic A to her for the rest of the year.
The lecture was so popular, in fact, that many students pressed Kathryn to record the lecture on video and sell DVDs of it.
If the function for Kathryn’s profit for selling DVDs of her college football presentation is 
, where 
is Kathryn’s profit and 
is the price per DVD, what price (in dollars) will maximize her profit?
Solution 1
To maximize the value of 
, we use the fact that the maximum value of a quadratic occurs when 
, where 
is the coefficient of the linear term and 
is the leading coefficient. Plugging in the given values, our answer is 
.
See Also
| 2005 iTest (Problems, Answer Key) | ||
| Preceded by: Problem 5 |
Followed by: Problem 7 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 • 31 • 32 • 33 • 34 • 35 • 36 • 37 • 38 • 39 • 40 • 41 • 42 • 43 • 44 • 45 • 46 • 47 • 48 • 49 • 50 • 51 • 52 • 53 • 54 • 55 • 56 • 57 • 58 • 59 • 60 • TB1 • TB2 • TB3 • TB4 | ||
