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Thread: I need to find the absolute extrema

  1. #1
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    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.
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  2. #2
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    Quote Originally Posted by ghow90 View Post
    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.
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  3. #3
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    I understand that but that was the first step in finding the absolute extrema
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