(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I sat my calculus exam at the end of june and of the questions on the paper required us to find the extreme values of the following equation:

[itex]g\left(x,y\right) = \left(x-1\right)\left(y-1\right)\left(x^{2} + y^{2} -2\right)[/itex]

3. The attempt at a solution

So i get:

[itex]\frac{\partial g}{\partial x} = 0 = \left(y-1\right)\left(3x^{2}-2x+y^{2} -2\right)[/itex]

[itex]\frac{\partial g}{\partial y} = 0 = \left(x-1\right)\left(3y^{2}-2y+x^{2} -2\right)[/itex]

From this I get 3 critical points [itex]\left(1,1\right), \left(1,-1\right), \left(-1,1\right)[/itex].

However in the answer sheet there are three more, but for the life of me I can't figure out how to get them. Is there a special trick that I'm missing out on? Any help would be much appreciated!

Final 3 points are included below for those who want to know them

[itex]\left(-\frac{1}{2},-\frac{1}{2}\right)[/itex]

[itex]\left(\frac{1}{2}-\frac{1}{\sqrt[]{2}},\frac{1}{2}+\frac{1}{\sqrt[]{2}}\right)[/itex]

[itex]\left(\frac{1}{2}+\frac{1}{\sqrt[]{2}},\frac{1}{2}-\frac{1}{\sqrt[]{2}}\right)[/itex]

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# Homework Help: Finding extreme values by partial differentiation.

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