Multivariable Max and min value problem.

[yaho8888]

Homework Statement

find local max min and saddle point.
f(x,y)= sin(x)sin(y), -pi<x<pi, -pi<y<pi

Homework Equations

none

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?

 

[HallsofIvy]

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?

 

[yaho8888]

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

 

[duke_nemmerle]

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?

 

[yaho8888]

solved!