#### Answer

No extreme and No saddle points

#### Work Step by Step

Given: $f_x(x,y)=2e^{2x} \cos y=0, f_y(x,y)=-e^{2x} \sin y=0$
Simplify the given two equations.
We find that there are no critical points.
Thus, we cannot apply the second derivative test as there are no critical points.