# Relative minimum,Relative maximum or saddle point?

I have function $f(x,y)=\sin(xy)$ in two variables. I found critical point $(0,0)$.

$f(x,y)$ has saddle point at $(0,0)$, because $D=f_{xx}(0,0)f_{yy}(0,0)-f_{xy}(0,0)<0$

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Hint: Well, notice $\cos(xy) = 0$ implies $xy = \pi \frac{2n+1}{2}$ for $n \in \mathbb{Z}$. Now you should be able to find the other critical points!
i got $\cos(xy)=0$ it means $xy=(2n\pm 1) \frac{\pi}{2}, n\in \mathbb{z}$ but i cant get value of D in integer at this point –  Siddhant Trivedi Nov 3 '12 at 7:04