The Function $f ( x , y ) = 4 - x ^ { 2 } - y ^ { 2 } - x y - x$

question 113

Multiple Choice

The function $f ( x , y ) = 4 - x ^ { 2 } - y ^ { 2 } - x y - x$ has one critical point. Determine its location and type.

• A) \(\left( - \frac { 2 } { 3 } , \frac { 1 } { 3 } \right)\) , saddle point
• B) \(\left( - \frac { 2 } { 3 } , \frac { 1 } { 3 } \right)\) , minimum point
• C) \(\left( - \frac { 2 } { 3 } , \frac { 1 } { 3 } \right)\) , maximum point
• D) \(\left( \frac { 1 } { 3 } , \frac { 2 } { 3 } \right)\) , saddle point
• E) \(\left( \frac { 1 } { 3 } , \frac { 2 } { 3 } \right)\) , minimum point
• F) \(\left( \frac { 1 } { 3 } , \frac { 2 } { 3 } \right)\) , maximum point
• G) \(\left( \frac { 1 } { 3 } , - \frac { 2 } { 3 } \right)\) , saddle point
• H) \(\left( \frac { 1 } { 3 } , - \frac { 2 } { 3 } \right)\) , minimum point

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