Find All the Local Maxima, Local Minima, and Saddle Points $f ( x , y ) = 2 x y - 5 x + 3 y$

question 78

Multiple Choice

Find all the local maxima, local minima, and saddle points of the function.
- $f ( x , y ) = 2 x y - 5 x + 3 y$

• A) \(\left\{ \left( - \frac { 3 } { 2 } , \frac { 5 } { 2 } \right) = \frac { 15 } { 2 } \right.\), saddle point
• B) \(\left\{ - \frac { 3 } { 2 } , - \frac { 5 } { 2 } \right) = \frac { 15 } { 2 }\), saddle point; \(\left\{ \left( \frac { 3 } { 2 } , \frac { 5 } { 2 } \right) = \frac { 15 } { 2 } \right.\), saddle point
• C) \(\left\{ - \frac { 3 } { 2 } , - \frac { 5 } { 2 } \right) = \frac { 15 } { 2 }\), local minimum; \(\left( \frac { 3 } { 2 } , \frac { 5 } { 2 } \right) = \frac { 15 } { 2 }\), local
• D) \(\left\{ \left( \frac { 3 } { 2 } , - \frac { 5 } { 2 } \right) = - \frac { 45 } { 2 } \right.\), local maximum

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