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

question 260

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 \(t = 0\)