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

question 27

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) \(f ( 2,1 ) = e ^ { 2 }\)

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