Maximizing Flux: Gauss's Theorem

[harrietstowe]

Homework Statement

Use the Divergence (Gauss's Theorem) to find the outward oriented closed surface (no boundary) for which the flux of F(x,y,z) = (16x-xz^2)i-(y^3)j-(zx^2)k is maximized.

Homework Equations

Gauss's Theorem

The Attempt at a Solution

divF = 16-z^2-3y^2-x^2 > 0 I think ?

 

[Dick]

Yes. But 16-z^2-3y^2-x^2 > 0 describes a volume. What's the surface that bounds that volume?