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The sum of two numbers is 16 . What is the largest possible product between these numbers

  • math -

    1 + 16
    2 + 14
    3 + 13
    4 + 12
    5 + 11
    6 + 10
    7 + 9
    8 + 8

    Which of those produce the greatest product?

  • math -

    y = x (16-x) = 16x - x^2
    dy/dx = 0 at max = 16 - 2x
    so
    x = 8
    8*8

  • math -

    or find vertex of that parabola (y = 16x-x^2) if you do not know derivatives.

    x^2 - 16 x = -y
    x^2 - 16 x + 64 = -y+64
    (x-8)^2 = (-y+64)
    x = 8

  • math -

    eight

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