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

question 335

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 \(t = \frac { \pi } { 4 }\)

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