Hi there. I've got some doubts about the maxima and minima on this function: $\displaystyle f(x,y)=x \sin y$. I've looked for critical points, and theres only one at (0,0). The thing is that when I've evaluate the second derivatives I've found that $\displaystyle f_{xx}=0$, then I have not a defined criteria on this case, cause the criteria that I have defines the concavity for $\displaystyle f_{xx}>0$ and $\displaystyle f_{xx}<0$. I don't know what happens when $\displaystyle f_{xx}=0$. I think the criteria fails, but I don't actually know what to do.

Bye there!