Question $10$:

Let $f(x,y,z)=(\frac{x^2}{2}-\frac{2x^6}{30}-\frac{4y^6}{30}-\frac{6z^6}{30})$

Let $S$ be a closed, non$-$intersecting surface in $R^3$ with a clearly defined inside and outside.

Let $A(S)$ be the outward normal flux of gradf through all of $S,$ that is$,$

$A(S)={}_S$gradf$*vec(n)$

Among all such surfaces, find the one $($that is$,$ write an equation for $S)$ that makes $A(S)$ as big as possible.