# Math Help - points of sruface closest to origin.

1. ## points of sruface closest to origin.

Problem :
Find the points on the surface $xy^2z^3=2$ that are closest to the origin.

I solved it for z:
$z=\sqrt[3]{\frac{2}{xy^2}}$.
and I said:
$f(x,y)=\sqrt[3]{\frac{2}{xy^2}}$
I stopped here.

2. For the solution using Lagrange multipliers see the attachment

check my arithmetic

3. Originally Posted by TWiX
Problem :
Find the points on the surface $xy^2z^3=2$ that are closest to the origin.

I solved it for z:
$z=\sqrt[3]{\frac{2}{xy^2}}$.
and I said:
$f(x,y)=\sqrt[3]{\frac{2}{xy^2}}$
I stopped here.
The square distance:

$D^2=x^2+y^2+z^2$

so:

$D^2=x^2+\frac{2}{xz^3}+z^2$

Which leaves you with the unconstrained minimisation of a function of two variables.

CB