I have this function:$$f(x,y)=\sqrt[21]{y^4+x^3-3x^2-4y^2}$$.
The domain of $f$ is all $\mathbb{R}^2$ or $\{(x,y)\in R^2: y^4+x^3\ge 3x^2+4y^2\}$?
If I consider $f(x,0)=\sqrt[21]{+x^3-3x^2}$ for $x\rightarrow +\infty$ or $x\rightarrow-\infty$, $f$ is unlimited up and down so max and min, if exist, are local.
If i calculate partial derivatives I found this points: $(0,\sqrt{2}),(0,-\sqrt{2}),(2,\sqrt{2}),(2,-\sqrt{2}),(2,0)$ but I have to consider also the origin?