Recent content by InsaneBraine

Thanks so much for your help!

I feel so stupid for misreading the problem. It clearly says that R consists of the interior AND the boundary. I somehow thought that R is only the interior. So the 5 points its asking for are basically (-1,-1) and the 4 points I found using Lagrange, correct?

So here's the original problem: [PLAIN]http://img141.imageshack.us/img141/2196/problemaz.jpg

Correction: Actually all 4 points I found using Lagrange lie on the boundary and not inside R (by definition). So what does the problem mean when it says that I should have found 5 points inside R?

I see. But the thing is in the next part for this problem we're supposed to use Lagrange multipliers to find the other points on the actual boundary x^2 + y^2 = 8. I found 4 other points. At the end of the problem it says that in total, you should have found 5 points inside R, but two of the...

So basically the region R doesn't play any role in this problem even though we're supposed to find the max/min points of the function within that interval? Could you please explain why that is so?

I don't think I have to do the latter part, since the problem only asks the point where it MIGHT have max/mins. So the gradient is: (x+1)i + (y+1)j. Now do I just set it equal to zero? If yes, then the only point I get is (-1, -1) and the region doesn't play a role. I could also plug in...

So what approach should I take if the points aren't on the boundary? How do I find them?

Homework Statement The function is f(x,y) = xy + x + y. The region R is defined as all the points lying inside x^2 + y^2 < 8. The problem asks us to find all the points in the region R where f may have a minimum or a maximum. Homework Equations Partial derivatives etc The Attempt at...