Calculus
posted by Britt .
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.

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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