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Min, Max or Saddle Point

  1. Nov 17, 2011 #1
    1. The problem statement, all variables and given/known data

    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?

    2. Relevant equations

    FxxFyy-Fxy2

    3. 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!
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Nov 17, 2011 #2

    I like Serena

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