Find the Absolute Extrema Of $$f ( x , y ) = 4 x ^ { 2 } + 2 y ^ { 2 } + 24 x - 8 \text { on the region }$$

question 110

Multiple Choice

Find the absolute extrema of $$f ( x , y ) = 4 x ^ { 2 } + 2 y ^ { 2 } + 24 x - 8 \text { on the region }$$ $$R = \left\{ ( x , y ) : x ^ { 2 } + y ^ { 2 } \leq 49 \right\} .$$

• A) absolute minimum: \(( - 3,0 , - 44 )\)
• absolute maximum: \(( - 6 , - \sqrt { 13 } , 306 )\)
• B) absolute minimum: \(( - 3,0 , - 44 )\)
• absolute maximum: \(( 0,0 , - 8 )\)
• C) absolute minimum: \(( 0,0 , - 8 )\)
• absolute maximum: \(( 3,0,100 )\)
• D) absolute minimum: \(( - 3,0 , - 44 )\)
• absolute maximum: \(( 7,0,356 )\)
• E) absolute minimum: \(( - 3,0 , - 44 )\)
• absolute maximum: \(( - 6 , \sqrt { 13 } , 18 )\)

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