$f(x,y) = xe^{-{x^3}+{y^3}}$ and
I am to find extrema values of that 2-variable function.
I come up with the point $P(3^{1/3},0,f(3^{1/3},0))$ is its only critical point.
I tried to apply second derivative test it is inconclusive.
Then, is there anything to do from this step on ?