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

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 $( 1,2 )$