Multivariable Max and min value problem.

amy

1. The problem statement, all variables and given/known data
find local max min and saddle point.
f(x,y)= sin(x)sin(y), -pilt;xlt;pi, -pilt;ylt;pi2. Relevant equations
none3. 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?  

    What do you mean by quot;fxfy= 0quot;?  The product?  A quot;critical pointquot; 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?  

    fx is the derivative of the function respect to x
fy ..................................................  ....... y
Where is sine 0?
at zero sin is zero  

                                   Originally Posted by yaho8888                   fx is the derivative of the function respect to x
fy ..................................................  ....... y
Where is sine 0?
at zero sin is zero                  
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?  

    solved!