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Math Help - Worded equation

  1. #1
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    Worded equation

    Find two positive numbers whose sum is 4 and such that the sum of te cube of the first an the square of the second is as small as possible.

    Thanks any help would be appreciated!
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  2. #2
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    Quote Originally Posted by scubasteve94 View Post
    Find two positive numbers whose sum is 4 and such that the sum of te cube of the first an the square of the second is as small as possible.

    Thanks any help would be appreciated!
    hi

    let x and y be the two positive numbers ,

    x+y = 4 -- 1

    let f(x)=x^3+y^2

    =x^3+(4-x)^2

    =x^3+x^2-8x+16

    f'(x)=3x^2+2x-8=(3x-4)(x+2)

    When f'(x)=0 , x=4/3 or x=-2

    x=4/3 is a local minimum and can be verified by taking the second derivative .
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  3. #3
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    Thank you!!
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