Originally Posted by

**Danny** First off, I believe you have a mistake in your derivatives.

$\displaystyle

\frac{\partial}{\partial x} \left(x^2 y^2 z^2 - \lambda(x^2+y^2+z^2-1) \right) = 2x y^2 z^2 - 2 \lambda x = 2x\left(y^2 z^2 - \lambda\right)

$

Similarly for the other two. Notice that I factored. This gives rise to

$\displaystyle

2x\left(y^2 z^2 - \lambda\right) = 0

$

$\displaystyle 2y\left(x^2 z^2 - \lambda\right) = 0$

$\displaystyle

2z\left(x^2 y^2 - \lambda\right) = 0

$

Now look at cases.

Let me ask, why use Lagrange multipliers when one of the variables can be easily eliminated?