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    erika75's Avatar
    erika75 Posts: 1, Reputation: 1
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    #1

    Sep 25, 2010, 10:54 PM
    Problem solving about quadratic functions
    Find the two real numbers whose sum is 4 and whose product is a maximum.
    Unknown008's Avatar
    Unknown008 Posts: 8,076, Reputation: 723
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    #2

    Sep 26, 2010, 12:35 AM

    Let the two real numbers be x and y.

    Their sum is given by:



    Then, you are told that their product is a maximum.

    Hence,



    Where I'll call k the maximum value.

    To get a maximum, x and y should both be positive (or both negative, but since their sum is positive, they cannot be both negative)

    What are the numbers which add up to 4?
    0 and 4
    1 and 3
    2 and 2

    Product:
    0
    3
    4

    I think you got your answer now :)
    BillRussell's Avatar
    BillRussell Posts: 8, Reputation: 1
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    #3

    Sep 30, 2010, 12:17 PM
    x+y = 4 from the first part.
    the product is f = xy
    substituting,
    f = x(4–x) = 4x – x²
    To maximize this, differentiate and set equal to 0 to find the max/min
    f' = 4 – 2x = 0
    2x = 4
    x = 2
    y = 2

    b
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