$$f(x,y) = x^4 + x^2 - y^4 - y^2$$
I've tried to find the partial derivatives and I get $2(2x^3+x)$ for $x\;$ and $\;-2(2y^3+y)\;$ for $y.$
Then I solved the equations $\;2(2x^3+x)=0\;$ when $\;x=0\;$ and $\;-2(2y^3+y)=0\;$ when $\;y=0.$
So extremum is $\;(0,0).$
Is that correct? Thanks