Find the Absolute Maximum and Minimum Values of the Function $f ( x , y ) = x y ;$

Multiple Choice

Find the absolute maximum and minimum values of the function on the given curve.
-Function: $f ( x , y ) = x y ;$ curve: $x ^ { 2 } + y ^ { 2 } = 49 , x \geq 0 , y \geq 0$ . (Use the parametric equations $x = 7$ cos $t , y = 7 \sin t$ .)

A) Absolute maximum: $\frac { 49 } { 4 }$ at $t = \frac { \pi } { 4 } ;$ absolute minimum: 0 at $t = 0$ and $t = \frac { \pi } { 2 }$
B) Absolute maximum: $\frac { 49 } { 4 }$ at $t = \frac { \pi } { 4 }$ ; absolute minimum: 0 at $t = 0$ and $t = \frac { \pi } { 4 }$
C) Absolute maximum: $\frac { 49 } { 2 }$ at $t = \frac { \pi } { 4 } ;$ absolute minimum: 0 at $t = 0$ and $t = \frac { \pi } { 2 }$
D) Absolute maximum: $\frac { 49 } { 2 }$ at $t = \frac { \pi } { 4 } ;$ absolute minimum: 0 at $t = 0$ and $t = \frac { \pi } { 4 }$