Maximize Flux: Vector Field (4x+2x^3z)i-y(x^2 +y^2)j -(3x^2z^2 +4y^2z)k

[Ragnar]

Given a vector field (4x+2x^3z)i-y(x^2 +y^2)j -(3x^2z^2 +4y^2z)k which closed surface has the greatest flux. I imagine that the divergence theorem palys a role but I'm not sure. please anwer ! This is killing me!

 

[HallsofIvy]

Since the problem is asking for a function (surface) that gives a maximum, this looks like a "calculus of variations" problem. What course is this in?