I never had seen this exercise, but I'm confused again, I don't know what I have to use.
I have the surface $S=\{(x,y,z)\in \mathbb{R}^3|xy+xz+yz=1,x>0,y>0,z>0\}$, is $S$ regular?. Then, if $S$ is regular, I have to found the higher value of $f$ defined by $f(x,y,z)=xyz$ where $(x,y,z)$ is in $S$.
Can anyone help me?