Problem :
Find the points on the surface $\displaystyle xy^2z^3=2$ that are closest to the origin.
I solved it for z:
$\displaystyle z=\sqrt[3]{\frac{2}{xy^2}}$.
and I said:
$\displaystyle f(x,y)=\sqrt[3]{\frac{2}{xy^2}}$
I stopped here.
Problem :
Find the points on the surface $\displaystyle xy^2z^3=2$ that are closest to the origin.
I solved it for z:
$\displaystyle z=\sqrt[3]{\frac{2}{xy^2}}$.
and I said:
$\displaystyle f(x,y)=\sqrt[3]{\frac{2}{xy^2}}$
I stopped here.