Locate the Local Minimum of the Function $f ( x , y ) = x y + \frac { 4 } { x } + \frac { 4 } { y }$

question 49

Multiple Choice

Locate the local minimum of the function. $f ( x , y ) = x y + \frac { 4 } { x } + \frac { 4 } { y }$

• A) \(\left( 4 ^ { \frac { 1 } { 3 } } , 4 ^ { \frac { 1 } { 3 } } , 3 \cdot 64 ^ { \frac { 2 } { 3 } } \right)\)
• B) \(\left( 4 ^ { \frac { 1 } { 3 } } , 4 ^ { \frac { 1 } { 3 } } , 12 ^ { \frac { 2 } { 3 } } \right)\)
• C) \(\left( 4 ^ { \frac { 1 } { 3 } } , 4 ^ { \frac { 1 } { 3 } } , 4 ^ { \frac { 2 } { 3 } } \right)\)
• D) \(\left( 4 ^ { \frac { 1 } { 3 } } , 4 ^ { \frac { 1 } { 3 } } , 3 \cdot 4 ^ { \frac { 2 } { 3 } } \right)\)
• E) \(\left( 4 ^ { \frac { 1 } { 3 } } , 4 ^ { \frac { 1 } { 3 } } , 3 \cdot 4 ^ { \frac { 1 } { 3 } } \right)\)

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