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Multivariable Max and min value problem.

  1. Mar 12, 2008 #1
    1. The problem statement, all variables and given/known data
    find local max min and saddle point.
    f(x,y)= sin(x)sin(y), -pi<x<pi, -pi<y<pi

    2. Relevant equations

    3. The attempt at a solution
    fx = cos(x)sin(y)
    fy= sin(x)cos(y)

    now how do I get the critical points, I know how to get max min and saddle point, but I don't know how to get critical points from this equation. when fx fy = 0, we got the critical point, I know there is (0,0), how do I find the others. I got another points (pi/2,pi/2), (-pi/2,-pi/2). is there more?
    Last edited: Mar 12, 2008
  2. jcsd
  3. Mar 13, 2008 #2


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    Staff Emeritus
    Science Advisor

    What do you mean by "fxfy= 0"? The product? A "critical point" is defined as a point where the function is not differentiable or where the partial derivatives are equal to 0. Since this function is obviously differentiable everywhere, its critical points are where cos(x)sin(y)= 0 and sin(x)cos(y)= 0. Since sin(x) and cos(x) can't be 0 at the same x, you must have either sin(x)=0 and sin(y)= 0 or cos(x)= 0 and cos(y)= 0. Where is sine 0?
  4. Mar 13, 2008 #3
    fx is the derivative of the function respect to x
    fy ......................................................... y
    Where is sine 0?
    at zero sin is zero
  5. Mar 13, 2008 #4
    Your critical points will occur at points where both partials are zero. on the given intervals, what values of x and y will make both fx and fy zero?
  6. Mar 14, 2008 #5
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