# Thread: I need to find the absolute extrema

1. ## I need to find the absolute extrema

This is the problem...

$\displaystyle f(x,y)=3xy-6x-3y+7$
on the closed triangular region, $\displaystyle R$, with vertices $\displaystyle (0,0), (3,0), and (0,5)$

I know I need to find the critical points so I found...

$\displaystyle Fx=3y-6$ and $\displaystyle Fy=3x-3$, right?

So to make $\displaystyle Fx=Fy=0$ the values of $\displaystyle x=1$ and $\displaystyle y=2$ so there is a critical point at $\displaystyle (1,2)$, right?

This is where I go blank on how to finish this.

2. Originally Posted by ghow90
This is the problem...

$\displaystyle f(x,y)=3xy-6x-3y+7$
on the closed triangular region, $\displaystyle R$, with vertices $\displaystyle (0,0), (3,0), and (0,5)$

I know I need to find the critical points so I found...

$\displaystyle Fx=3y-6$ and $\displaystyle Fy=3x-3$, right?

So to make $\displaystyle Fx=Fy=0$ the values of $\displaystyle x=1$ and $\displaystyle y=2$ so there is a critical point at $\displaystyle (1,2)$, right?

This is where I go blank on how to finish this.
Yes, however, the absolute extrema might occur on the boundaries rather than at a critical point.

3. I understand that but that was the first step in finding the absolute extrema