- #1
Gekko
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- 0
Homework Statement
Find all critical points and classify them
Homework Equations
f(x,y) = sin(x)sin(y)sin(x+y)
0<=x,y<=Pi
The Attempt at a Solution
fx=sinysin(2x+y) and fy=sinxsin(2y+x)
Therefore critical points are at:
x=Pi/3(2n-m) , y=Pi/3(2m-n) where n>=1, m<=2, n,m belong to integer set (Z)
fxx = sin(2x+2y)-sin(2x)
fyy = sin(2x+2y)-sin(2y)
fxy = sin(2x+2y)
Now, to classify the critical points I was simply going to test for:
fxxfyy-fxy^2
If <0 it is a saddle point etc and substitute for x the definitions above to obtain the equation we can use to classify with
Is this correct? Is there a better way? Would greatly appreciate comments. Thanks