Find and Classify the Critical Points of the Function F(x $\pi$

Multiple Choice

Find and classify the critical points of the function f(x, y) = x sin y.

A) local maxima at (0, n $\pi$ ) for even integers n, local minimum at (0, n $\pi$ ) for odd integers n
B) local minima at (0, n $\pi$ ) for even integers n, local maximum at (0, n $\pi$ ) for odd integers n
C) saddle points at all points (0, n $\pi$ ) for integers n
D) only critical point is (0, 0) , a saddle point
E) local minima at (0, n $\pi$ ) for nonzero integers n, saddle point at (0, 0)