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Math Help - Maximum

  1. #1
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    Joined
    Feb 2009
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    20

    Maximum

    The sum of two positive numbers is 5. What is the value of the larger number if the product of the smaller number and the cube of the larger is a maximum?

    a. 5
    b. 15/4
    c. 5/4
    d.1
    e.0
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  2. #2
    Member
    Joined
    Apr 2009
    Posts
    166
    So a + b = 5 and some f(x) = a(b)^3.

    a = 5-b

    f(x) = (5-b)(b^3) = 5b^3 - b^4

    Max occurs at f'(x) = 0

    15b^2 - 4b^3 = 0

    b^2(15-4b) = 0

    b = 0, 15/4

    f''(15/4) < 0

    Answer 15/4
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