I have to find the region $E$ where
$ \iiint_E (1-x^2 - 2y^2 - 3z^2) dV $
has maximum value, but I'm not sure how to start.
I was thinking of getting the derivative of the integral and then finding the extrema with the usual $f_x = 0, f_y = 0$ equation system, but even if I get the second derivative of it, I'm stuck with a single integral and I'm not sure if that's right.