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f(x, y) = 3ycos x, 0 ≤ x ≤ 2π

Finding the locla minima, maxima, and saddle points. Having difficulty as so far I have:
Fx = -3ysinx
Fy = 3cosx
Fxx = -3ycosx
Fyy = 0
Fxy = -3sinx

I have set both Fx and Fy equal to 0 but am not too sure about the critical points, which are my biggest problem. I fell like they would be set to x = 0, pi and y = 0 for Fx, and for Fy would be x = pi/2 and 3pi/2.

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