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Math Help - Calculus problem example

  1. #1
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    Calculus problem example

    I'll be taking pre-calc soon, and I've been wondering about something.

    I know that some problems can be solved with algebra.

    Example:

    Tickets for a school play are $12 for adults and $8 for students. The school sold 200 tickets for Friday night. If the school earned $1,860 for the show, how many $12 tickets did they sell.

    I can solve this example writing

    12x + 8y = 1860
    x + y = 200
    (Can solve by elimination or substitution)

    So, I was wondering if anyone could give me an example of a problem that cannot be solved by using only Algebra and must us Calculus to solve it.
    Last edited by Chris712; July 13th 2012 at 10:30 PM.
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  2. #2
    Senior Member BAdhi's Avatar
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    Re: Calculus problem example

    How about optimization problems such as this
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  3. #3
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    Re: Calculus problem example

    The first problem in BAdhi's link can be solved without calculus. By AM-GM inequality, \frac{x + 2y}{2} \ge \sqrt{2xy} \Rightarrow \frac{500}{2} \ge \sqrt{2xy}. Equality occurs if and only if x = 2y (x = 250, y = 125).


    Other optimization problems don't have easy algebraic/geometric solutions and therefore must be solved using calculus. For example, find the area bounded by the x-axis and f(x) = \sin {2x}, 0 \le x \le \pi.
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