I'm stuck on the following question(adsbygoogle = window.adsbygoogle || []).push({});

"Find the maximum and minimum values of f(x,y,z) = [tex] x^2y^2-y^2z^2 + z^2x^2[/tex] subject to the constraint of [tex] x^2 + y^2 + z^2 = 1[/tex] by using the method of lagrange multipliers.

Write the 4 points where the minimum value is achieved and the 8 points where the max is achieved"

So far, I've managed to calculate the gradient for both formulae and have the resulting equations:

[tex]2xy^2 + 2z^2x = \lambda(2x)[/tex]

[tex]2x^2y - 2z^2y = \lambda(2y)[/tex]

[tex]2x^2z - 2y^2z = \lambda(2z)[/tex]

Do I just substitute these equations in turn into the constraint equation and determine what the points are that satisfy it?

Also, how do you find out if a point is a local max/min when you know the critical point when looking at a case like this?

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# Lagrange multipliers Q

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