Well, I have this multivariable calculus optimization problem. It says: Decompose a positive number on three non negative summands so that the product of them is maximum.

I thought of something like

$\displaystyle w=x+y+z$, $\displaystyle w>0, x \geq{}0 , y \geq{}0 , z \geq{}0 $

$\displaystyle f(x,y,z)=xyz$

$\displaystyle f_x=yz,f_y=xz,f_z=xy$

The thing is I don't see any maximum here, clearly I'm not setting the things right.