Find and Classify the Relative Extrema and Saddle Points of the Function

Multiple Choice

Find and classify the relative extrema and saddle points of the function $f ( x , y ) = e ^ { - 2 x } \sin 4 y$ for $x \geq 0$ and $0 \leq y \leq \frac { \pi } { 2 }$ .

A) None
B) Relative maximum $f \left( 0 , \frac { \pi } { 8 } \right) = 1$
C) Saddle point $( 0,0,0 )$
D) Relative minimum $f \left( 0 , \frac { \pi } { 4 } \right) = 0$