Find absolute extrema of...
f(x,y)=xy-2x-y+6 on closed triangular region with vertices (0,0), (0,8) and (4,0). I need to know what the etremum are and if max or min and at what points these occur.
What you "need to know" is how to find max and min!
Whoever gave you this problem clearly expects you to know that if a max or min occurs in the interior of a region in two dimensions the two partial derivatives must both be 0. Of course, the max and/or min might be on a boundary. The boundary consists of the three line segments bounding the triangle. Write each with y as a function of x. If a max or min occurs in the interior of a segment, must be where the derivative of y with respect to x 0. Finally, a max or min may occur at the boundary of an interval and those boundaries are the three vertices of the triangle.