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Math Help - Word Problems

  1. #1
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    Word Problems

    1) For what number between 0 and 1 is the difference between its square and its cube greatest?
    Last edited by blurain; November 23rd 2007 at 02:33 PM.
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  2. #2
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    Part a)

    Solution: “the difference between its square and its cube” means x^2x^3. “the greatest” implies we’re looking for a max (or at least an extremum). “between 0 and 1” means we’re on the interval [0, 1]. So

    f(x) = x^2x^3 implies f '(x) = 2x3x^2;
    this is 0 if x = 0 or 2 = 3x
    meaning x = 2/3

    Our values are:

    f(0) = 0, f(1) = 0, f(2/3) = 4/9 - 8/27 = 4/27
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