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Maxima and minima of functions of two variables

  1. Nov 5, 2012 #1
    1. The problem statement, all variables and given/known data

    Locate all relative maxima, relative minima ,and saddle points if any.

    f(x,y)=ysinx

    fx(x,y)=ycosx

    fy(x,y)=sinx

    ycosx=0 sinx=0
    y=0 x=0,∏,2∏... up until infinity
    Critical points at (0,0),(∏,0),(2∏,0)....

    fxx(x,y)=-ysinx

    fyy(x,y)= cosx

    fxx*fyy-f(x,y)2→0-0=0 ∴ no relative extrema,

    however the book says that fxx*fyy-f(x,y)2=-1 which means saddle point.

    I dont understand if y is = to zero.. the function ysinx will always be zero..

    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Nov 5, 2012 #2
  4. Nov 5, 2012 #3
    Sorry that was a typo, but still doesn't help regardless.
     
  5. Nov 5, 2012 #4

    SammyS

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    Isn't fy(x,y) = sin(x) ?

    Then what is fyy(x,y) ? Isn't it zero?

    Also, What is fxy(x,y) ?

    You need fxx*fyy-(fxy)2 , not fxx*fyy-f(x,y)2
     
    Last edited: Nov 5, 2012
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