I need to find the absolute extrema

• Apr 7th 2010, 05:27 AM
ghow90
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.
• Apr 7th 2010, 01:37 PM
HallsofIvy
Quote:

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.
• Apr 7th 2010, 01:47 PM
ghow90
I understand that but that was the first step in finding the absolute extrema