- #1

java22

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## Homework Statement

f(x,y) = x

^{2}-4xy+5y

^{2}-8y ; enclosed by the triangular region (0,0), (3,0), and (3,3)

Find the absolute maximum and minimum

## Homework Equations

N/A

## The Attempt at a Solution

First I took the partial derivatives with respect to x and y:

fx = 2x - 4y

fy = -4x + 10y -8

I then set both of these equal to zero and solved them as a system of equations. This gives the critical point of (8,4)

Now, this is where I'm lost. Since the critical point (8,4) doesn't exist in the bounded region given, is the problem simply not solvable, and there are no absolute minima or maxima? I assume I am going about it wrong because calculus is never that easy.