Calculus

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Minimize S=x+2y with xy=2 and
both x and y > 0.

Can somebody explain to me in words and numbers how to do this problem.

  • Calculus -

    First change xy = 2 to y=2/x

    then
    S = x + 2y
    =x + 2(2/x)
    = x + 4/x

    then S' = 1 - 4/x^2
    = 0 for a max/min of S

    solving you get x = ± 2 but x > 0
    so x = 2 and y = 2/2 = 1

    then S = 2 + 2(1) = 4

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