(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

f(x,y)=xy+(144/x)+(12/y)

f has a relative minimum at ( , , )

2. Relevant equations

Partial derivatives

3. The attempt at a solution

f_{x}=y-(144/x^2)

f_{y}=x-(12/y^2)

I setted these to zero. Multiplies both sides so there is no fraction.

Came out to be something like~~~ x^{2}y-144=0

xy^{2}-12=0

then did the factoring stuff and got

x^{2}-12xy^{2}=0

This tells me that the critical point is (0,0), but this is the wrong answer.

PLEASE TELL ME WHAT I AM DOING WRONG.

THANK YOU SO MUCH TO THOSE WHO HELP. THIS FORUM IS HELPING ME BECOME A BETTER MATHMATICIAN AND THEREFORE, MY TEST GRADES ARE GOING UP. THANK YOU.

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# Classifying Critical Points

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