Chapter 14: Partial Derivatives - Section 14.7 - Extreme Values and saddle Points - Exercises 14.7 - Page 843: 24

No extreme and No saddle points

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.