Find the Absolute Maximum and Minimum Values of the Function $f ( x , y ) = x ^ { 2 } + 2 y ^ { 2 } ;$

Multiple Choice

Find the absolute maximum and minimum values of the function on the given curve.
-Function: $f ( x , y ) = x ^ { 2 } + 2 y ^ { 2 } ;$ curve: $\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 16 } = 1 , x \geq 0$ , $y \geq 0$ . (Use the parametric equations $x = 3$ cos $t$ , $y = 4 \sin t$ .)

A) Absolute maximum: 32 at $t = \frac { \pi } { 2 }$ ; absolute minimum: 9 at $t = 0$
B) Absolute maximum: 16 at $t = \frac { \pi } { 2 } ;$ absolute minimum: 18 at $t = 0$
C) Absolute maximum: 16 at $t = \frac { \pi } { 2 } ;$ absolute minimum: 9 at $t = 0$
D) Absolute maximum: 32 at $t = \frac { \pi } { 2 } ;$ absolute minimum: 18 at $t = 0$