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.

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- Mar 17th 2013, 01:15 PMsluggerbrothHELP!!!---find absolute extrema of...
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. - Mar 17th 2013, 02:15 PMHallsofIvyRe: HELP!!!---find absolute extrema of...
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. - Mar 17th 2013, 02:30 PMsluggerbrothRe: HELP!!!---find absolute extrema of...
thanks but i am going to need more guidance? help again please?

- Mar 17th 2013, 03:11 PMHallsofIvyRe: HELP!!!---find absolute extrema of...
I am confused- this is a fairly standard "Calculus of Several Variables". Are you saying you do not know how to find a partial derivative?

- Mar 17th 2013, 03:31 PMsluggerbrothRe: HELP!!!---find absolute extrema of...
Partial derivative I can handle but how to deal with boundry?