The problem I'm looking asks us to find the absolute max and min of $f(x,y)$, which is $-x + 2y - 3z$. The constraint given is $x^2+2y^2+3z^2\le \frac{3}{2}$.
Because the constraint has an inequality, this means we are considering the boundary of the constraint, right? IIRC, the gradient of f (expressed as $\nabla f$) should equal 0...but $\nabla f$ is $<-1,2,-3>$...what does imply for the absolute max and min? (I found the max and min values given the constraint $x^2+2y^2+3z^2=\frac{3}{2}$, not sure if that is applicable to this situation).