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Math Help - I need to find the absolute extrema

  1. #1
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    I need to find the absolute extrema

    This is the problem...

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

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

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

    So to make Fx=Fy=0 the values of x=1 and y=2 so there is a critical point at (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...

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

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

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

    So to make Fx=Fy=0 the values of x=1 and y=2 so there is a critical point at (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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