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: $x ^ { 2 } + y ^ { 2 } = 49 , y \geq 0$ . (Use the parametric equations $x = 7 \cos t , y = 7 \sin t$ .)

A) Absolute maximum: $7 \sqrt { 2 }$ at $t = \frac { \pi } { 4 }$ ; absolute minimum: $- 7 \sqrt { 2 }$ at $t = \frac { 3 \pi } { 4 }$
B) Absolute maximum: $7 \sqrt { 2 }$ at $t = \frac { \pi } { 4 }$ ; absolute minimum: $- 7$ at $t = \pi$
C) Absolute maximum: 7 at $t = \frac { \pi } { 2 } ;$ absolute minimum: $- 7 \sqrt { 2 }$ at $t = \frac { 3 \pi } { 4 }$
D) Absolute maximum: 7 at $t = \frac { \pi } { 2 }$ ; absolute minimum: $- 7$ at $t = \pi$