I am trying to find and classify the stationary points of this function. I have make some calculations but it have been very complex. If you have an idea and solution i will be happy. Thank you
2026-04-09 09:25:08.1775726708
Stationary Points of A Function of Two Variables
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i have got the following system $$8+8x_1-8x_2-8x_1x_2+2x_2^2+2x_1x_2^2=0$$ $$-4-8x_1-4x_1^2+2x_2+4x_1x_2+2x_1^2x_2=0$$ Have you got this? solving the first equation for $x_1$ we get $$x_1(8-8x_2+2x_2^2)=8x_2-8-2x_2^2$$ have you got this? a last comment, your function can be written as $$f(x_1,x_2)=(-4-2x_1+x_2+x_1x_2)(-2x_1+x_2+x_1x_2)$$