Find the Absolute Extrema Of $f ( x , y ) = 4 x ^ { 2 } + 8 x y - 48 x - 8 y \text { on the region bounded }$

question 111

Multiple Choice

Find the absolute extrema of $f ( x , y ) = 4 x ^ { 2 } + 8 x y - 48 x - 8 y \text { on the region bounded }$ by the square with vertices $( 0,0 ) , ( 7,0 ) , ( 0,7 )$ , and $( 7,7 )$ .

• A) absolute minimum: \(( 0,7 , - 56 )\)
• absolute maximum: \(( 0,0,0 )\)
• B) absolute minimum: \(( 0,7 , - 56 )\)
• absolute maximum: \(( 7,7,196 )\)
• C) absolute minimum: \(( 1,5 , - 44 )\)
• absolute maximum: \(( 0,0,0 )\)
• D) absolute minimum: \(( 6,0 , - 144 )\)
• absolute maximum: \(( 7,7,196 )\)
• E) absolute minimum: \(( 6,0 , - 144 )\)
• absolute maximum: \(( 0,0,0 )\)

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