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

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