Find the Extreme Values of the Function Subject to the Given

question 327

Multiple Choice

Find the extreme values of the function subject to the given constraint.
- $$f ( x , y ) = x ^ { 2 } y , x ^ { 2 } + 2 y ^ { 2 } = 6$$

• A) Maximum: 4 at \(( 2,1 )\); minimum: \(- 4\) at \(( - 2 , - 1 )\)
• B) Maximum: 18 at \(( \pm 3,2 )\); minimum: \(- 18\) at \(( \pm 3 , - 2 )\)
• C) Maximum: 4 at \(( \pm 2,1 )\); minimum: \(- 4\) at \(( \pm 2 , - 1 )\)
• D) Maximum: 18 at \(( 3,2 )\); minimum: \(- 18\) at \(( - 3 , - 2 )\)

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