Find the maximum and minimum values of a tri-variable function

I'm not sure if this is another Lagrange Multiplier question or not, but so far this question has me a little confused.

Let $\displaystyle R$ be the region in $\displaystyle R^3$ which is inside the ellipsoid $\displaystyle 3x^2+3y^2+z^2=28$ and above the paraboloid $\displaystyle z=x^2+y^2$. Find the maximum and minimum values of the function $\displaystyle f(x,y,z)=2x^3-2y^3+z^2$ on the region $\displaystyle R$.

HINT: $\displaystyle R$ is inside the cylinder $\displaystyle x^2+y^2=4$.

It's probably the wording again (I always trip on word problems), but it probably shouldn't cause too much trouble.