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## Homework Statement

Decide between a minimum, maximum, or saddle point for:

(a) F=-1+4(e

^{x}-x)-5xsin(y)+6y

^{2}at the point x=y=0

(b) F=(x

^{2}-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?

## Homework Equations

F

_{xx}F

_{yy}-F

_{xy}

^{2}

## The Attempt at a Solution

For part a,

I got the point is at a minimum because

F

_{xx}F

_{yy}-F

_{xy}

^{2}=23, which is greater than 0, and so are both F

_{xx}and F

_{yy}(4 and 12 respectively).

For part b,

I got the point is at a maximum because

F

_{xx}F

_{yy}-F

_{xy}

^{2}=2, which is greater than 0, but both F

_{xx}and F

_{yy}are negative (-2 and -1 respectively).

Am I thinking correctly? Thanks!