Minimize S=x+2y with xy=2 and

Question

both x and y > 0.

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

Answer 1

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