I was given the following problem:
Find the absolute extrema of the function \(f(x,y)=x^2+y^2-4xy\) on the region bounded by \(y=x\), \(y=-3\) and \(x=3\).
This is my work so far.
What I'm having trouble with is figuring out the endpoints for my region. In order to know if I actually found a maximum, I need the endpoints.
Also, I'm not sure where to go from here. Do I take the derivative with respect to y of my \(j(y)\) function?
I know that at the end I can compare all my answers to find my maximum and minimum. I'm just not sure how to find the rest of my candidates.
Find the absolute extrema of the function \(f(x,y)=x^2+y^2-4xy\) on the region bounded by \(y=x\), \(y=-3\) and \(x=3\).
This is my work so far.
What I'm having trouble with is figuring out the endpoints for my region. In order to know if I actually found a maximum, I need the endpoints.
Also, I'm not sure where to go from here. Do I take the derivative with respect to y of my \(j(y)\) function?
I know that at the end I can compare all my answers to find my maximum and minimum. I'm just not sure how to find the rest of my candidates.
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