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## Homework Statement

find two positive numbers with product of 200 such that the sum of one number and twice the second number is as small as possible.

**2. The attempt at a solution**

my work:

xy=200 ==> y = 200/x

x+2y = s (what we need to minimize)

x+2(200/x) =s

x+400x^-1 = s

1-400x^-2 = ds/dx

(x^2-400)/x^2 = dx/dx

(x-200)(x+200)/(x^2) = ds/dx

crit numbers: 0, 200, -200 (not included because the domain is x>0)