- #1

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[tex]f(x,y)=sin(x)+sin(y)+sin(x+y)[/tex]

where:

[tex]0\leq x \leq 2\Pi[/tex]

[tex]0\leq y \leq 2\Pi[/tex]

Partial derivatives:

[tex]f_{x}=cos(y)+cos(x+y)[/tex]

[tex]f_{y}=cos(x)+cos(x+y)[/tex]

[tex]f_{xx}=-sin(x+y)[/tex]

[tex]f_{xy}=-sin(y)-sin(x+y)[/tex]

[tex]f_{yy}=-sin(x+y)[/tex]

Now I have no clue how to get all the critical points. I simplified it using fx=0, fy=0, to get fx=fy. Equating and simplifying I got cos(x)=cos(y), x=y.

Now this is where I get lost. How do you pick points to try and solve the equations? I could say that cos(x)=cos(y), then cos(x)-cos(y)=0. So you could pick x or y to be pi/2 or 3pi/2.

However the solution manual to my textbook does not use any of these points...so how does this work?