Find the global maximum and minimum of f(x,y) = (x^2) -2xy + 2y on the domain x ≥ 0, y ≥ 0 and y ≤ 2-x
Ok, so lets do the second derivative test.
fxx = 2
fyy = 0
Also, my previous points were wrong. It was (1,1), not (1,-1).
So, what do I do now? Now that I've taken the second derivatives? What do they show?
Ok, so here is what I did.
Found the critical point (1,1). f(1,1) = 1
The Discriminant showed it is a saddle point.
Found the edge points to be (2,0), (0,2) and (0,0) (Is this correct?)
Evaluating the f(edge points), I got 4, 4 and 0 respectively.
So.....global maximum is 4 at (2,0) and (0,2)? Global minimum is 0 at (0,0)?
Saddle point isn't max or min right? Also, is it ok if the maximum happens at 2 points? Is all this correct?