SOLUTION: Assume x > 0 and y > 0. If the square root of xy = 5, what is the smallest positive sum of 4x + y?

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Question 1059185: Assume x > 0 and y > 0. If the square root of xy = 5, what is the smallest positive sum of 4x + y?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Define Z=4x%2By
You know that,
sqrt%28xy%29=5
xy=25
x=25%2Fy
Substituting,
Z=4%2825%2Fy%29%2By
Z=100%2Fy%2By
Now Z is a function of one variable.
Find the derivative and set it equal to zero to find the minimum.
dZ%2Fdy=-100%2Fy%5E2%2B1=0
100%2Fy%5E2=1
y%5E2=100
y=10
So then,
x=25%2F10
x=5%2F2
and
Z=4%285%2F2%29%2B10
Z=10%2B10
Z=20
You should technically calculate the second derivative and show that the extremum is a minimum.