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Min, Max or Saddle Point

  • #1

Homework Statement



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?

Homework Equations



FxxFyy-Fxy2

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!

Homework Statement





Homework Equations





The Attempt at a Solution


Homework Statement





Homework Equations





The Attempt at a Solution

 

Answers and Replies

  • #2
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