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$f(x, y) = x^4 + y^4 - 4xy + 3$ I solved it and I got two minimum points $(1,1)$ and $(-1,-1)$ and I got $(0,0)$ as my saddle point but I'm suspecting that the function doesn't have a saddle point are my answers right?

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  • $\begingroup$ Wolfram Alpha agrees with your computation (as opposed to your suspicion). $\endgroup$ – Theo Bendit Oct 14 '19 at 5:23
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Let be $y=x$ then

$$ g(x) = f(x,x) = - 4x^2 +2x^4 + 3 $$ which has a maximum at $x=0$. Let be $y=-x$, then $$ h(x) = f(x, - x) = 4x^2 +2x^4 + 3 $$ which has a minimum at $x=0$. Therefore your function does have a saddle point at $(0,0)$.

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