Use Lagrange Multipliers to Find the Given Extremum $x$ And $y$ Are Positive

Multiple Choice

Use Lagrange multipliers to find the given extremum. Assume that $x$ and $y$ are positive. Minimize $f ( x , y ) = e ^ { xy }$ Constraint $x ^ { 2 } + y ^ { 2 } - 8 = 0$

A) $f ( 2,2 ) = e ^ { 4 }$
B) $f ( 1,1 ) = e ^ { 1 }$
C) $f ( 3,1 ) = e ^ { 3 }$
D) $f ( 4,2 ) = e ^ { 8 }$
E) $f ( 2,1 ) = e ^ { 2 }$