Did you notice that your second constraint can be nicely simplified with your first constraint? Rather simplifies the whole problem, in fact.
Would all be helping me out here alot
Find the local maxima and minima of the following function:
Subject to the constraints:
The answers I got were:
with ... This gives a local maximum.
with ... This gives a local minimum.
I hope these are right. If I have made an error, and you want my working just reply... thanks!!
Haha, I doubt myself all the time - although the fact that they are nice answers gives me some confidence. I determined local max/min by doing the whole Bordered hessian matrix technique, confirming they weren't non-degenerate critical points, and then checking that , where is the tangent vector at that point, was always positive to give a local min, negative to give a local max....
Well, there you go. If you can even SAY "Bordered Hessian" I have to think that you ahve at least a little clue. As long as you used the right criteria for various minors, you have it! Did you? :-)