Find the Extreme Values of the Function Subject to the Given

question 169

Multiple Choice

Find the extreme values of the function subject to the given constraint.
- $$f ( x , y ) = y ^ { 2 } - x ^ { 2 } , \quad x ^ { 2 } + y ^ { 2 } = 16$$

• A) Maximum: 32 at \(( 0 , \pm 4 \sqrt { 2 } )\); minimum: \(- 32\) at \(( \pm 4 \sqrt { 2 } , 0 )\)
• B) Maximum: 16 at \(( 0 , \pm 4 )\); minimum: \(- 32\) at \(( \pm 4 \sqrt { 2 } , 0 )\)
• C) Maximum: 32 at \(( 0 , \pm 4 \sqrt { 2 } )\); minimum: \(- 16\) at \(( \pm 4,0 )\)
• D) Maximum: 16 at \(( 0 , \pm 4 )\); minimum: \(- 16\) at \(( \pm 4,0 )\)

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