Find all the critical points of
I get (3,0) and (-1,0) Did I do the question correctly? Please and thanks.
No, I was not but I just discovered it and will very well press. Also, please if I take this a step further,
Am I correct in my calculations that (3,3) is a local minimum and (-1,-1) is neither seeing as for (-1,-1) => (f_xx)(f_yy)-[f_xy]^2=0
Aha! You are taking it to the next level!
Not quite.
Yes, (3,3) is a local minimum, but as yet (-1,-1) is inconclusive.
See for instance: Second partial derivative test - Wikipedia, the free encyclopedia
This means that (-1,-1) could still be either a minimum, a maximum, or a saddle point.