Decide between a minimum, maximum, or saddle point for:
(a) F=-1+4(ex-x)-5xsin(y)+6y2 at the point x=y=0
(b) F=(x2-2x)cos(y) with stationary point at x=1, y=pi
The professor was a bit confusing, so I did it the way I remember from Calc, but am unsure of whether I went the right direction or not... Ideas?
The Attempt at a Solution
For part a,
I got the point is at a minimum because
FxxFyy-Fxy2=23, which is greater than 0, and so are both Fxx and Fyy (4 and 12 respectively).
For part b,
I got the point is at a maximum because
FxxFyy-Fxy2=2, which is greater than 0, but both Fxx and Fyy are negative (-2 and -1 respectively).
Am I thinking correctly? Thanks!