points of sruface closest to origin.

**TWiX** · January 16th 2010, 08:29 AM

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.

**Calculus26** · January 16th 2010, 09:52 AM

For the solution using Lagrange multipliers see the attachment

check my arithmetic

**CaptainBlack** · January 16th 2010, 10:27 AM

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

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