Find the Absolute Extrema of the Function $f ( x , y ) = ( 3 x - y ) ^ { 2 } \text { over the triangular }$

question 21

Multiple Choice

Find the absolute extrema of the function $f ( x , y ) = ( 3 x - y ) ^ { 2 } \text { over the triangular }$ region in the $x y$ -plane with vertices $( 2,0 ) , ( 0,2 )$ , and $( 1,3 )$ .

• A) absolute maximum: 36 at \(( 2,0 )\)
• absolute minimum: 0 at \(( 1,3 )\) and along the line \(y = 3 x\)
• B) absolute maximum: 1 at \(( 1,2 )\)
• absolute minimum: 0 at \(( 1,3 )\) and along the line \(y = 3 x\)
• C) absolute maximum: 4 at \(( 0,2 )\)
• absolute minimum: 0 at \(( 1,3 )\) and along the line \(y = 3 x\)
• D) absolute maximum: 36 at \(( 2,0 )\)
• absolute minimum: 4 at \(( 0,2 )\)
• E) absolute maximum: 36 at \(( 2,0 )\)
• absolute minimum: 1 at \(( 1,2 )\)