Use Lagrange Multipliers to Find the Maximum Value of the Function

question 1

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) \[f ( x , y ) = 9\]