I have to find max,min of $f(x,y,z)=1/(3x^2 +z^2)$constrained on a region $D$
$D =\{x^2+z^2-y^2-3\le 0\}$ -> $g(x,y,z)=x^2+z^2-y^2-3=0$
- I used the Lagrange multiplier method: and I got the points
$P_1(\pm\sqrt{3},0,0)$->$f(P_{1})=1/9$
$P_2(0,0,\pm\sqrt{3})$->$f(P_{2})=1/3$
- So My question is : (with the fact that $f(x,y,z)$ doesn't contain a $y$ )It is more correct to write the points with $y = 0$ or with $y=y$, like that:
$P_{1a}(\pm\sqrt{y^2+3},0,0)$->$f(P_{1a})=1/(3y^2+9)$
$P_{2a}(0,0,\pm\sqrt{y^2+3})$->$f(P_{2a})=1/(y^2+3)$