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

question 151

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 \(t = \pi\)

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