Calculus 3... extrema

[chunkyman343]

I have to find the extrema for the following function:
x^3+3xy+y^3

this is what i have:
fx(x,y)=3x^2+3y
fy(x,y)=3x+3y^2

then im lost on what to do next find fx(0) &fy(0) or find a determinant

[maverick_starstrider]

Um... This section is for discussions of learning materials (i.e. textbooks and stuff) not homework problems. I'm sure a mod will move it soon. Anyways, consider that, just as in single varibale calculus, When the GRADIENT of a function is zero, you have a critical point (just like when the derivative is zero in single variable).

[chunkyman343]

oops srry about that

[maverick_starstrider]

That's fine. Are you making any headway with the problem?

[chunkyman343]

i think i figured it out.... i have a relative max at (-1,-1,1)