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

question 311

Multiple Choice

Find the absolute maximum and minimum values of the function on the given curve.
-Function: $f ( x , y ) = x y ;$ curve: $\frac { x ^ { 2 } } { 36 } + \frac { y ^ { 2 } } { 81 } = 1 , y \geq 0$ . (Use the parametric equations $x = 6 \cos t , y = 9 \sin t$ .)

• A) Absolute maximum: \(\frac { 27 } { 2 }\) at \(t = \frac { \pi } { 4 } ;\) absolute minimum: \(- \frac { 27 } { 2 }\) at \(t = \frac { 3 \pi } { 4 }\)
• B) Absolute maximum: \(\frac { 27 } { 2 }\) at \(t = \frac { \pi } { 4 }\); absolute minimum: \(- 27\) at \(t = \frac { 3 \pi } { 4 }\)
• C) Absolute maximum: 27 at \(t = \frac { \pi } { 4 } ;\) absolute minimum: \(- \frac { 27 } { 2 }\) at \(t = \frac { 3 \pi } { 4 }\)
• D) Absolute maximum: 27 at \(t = \frac { \pi } { 4 } ;\) absolute minimum: \(- 27\) at \(t = \frac { 3 \pi } { 4 }\)

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