Answer
No extrema and no saddle points
Work Step by Step
Since, we have $f_x(x,y)=2e^{2x} \cos y=0, f_y(x,y)=-e^{2x} \sin y=0$
Since, $e^{2x} \ne 0$
and the functions $\sin y\ne 0$ and $\cos y \ne 0$ (for the same $y$ value).
Thus, we get the result: there are no critical points or saddle points.
