Use Lagrange Multipliers to Find the Maximum Value of the Function

Multiple Choice

Use Lagrange multipliers to find the maximum value of the function subject to the given constraint. $$f ( x , y ) = 8 x ^ { 2 } - 4 y ^ { 2 } , 8 x ^ { 2 } + 4 y ^ { 2 } = 9$$

A) $f ( x , y ) = 8$
B) $f ( x , y ) = \frac { 1 } { 4 }$
C) $f ( x , y ) = \frac { 1 } { 9 }$
D) $f ( x , y ) = \frac { 1 } { 8 }$
E) $$f ( x , y ) = 9$$