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

Question

Quizplus · Accepted Answer

The function does not have a local maximum, minimum, or saddle point due to its linear terms in x and y, making the choices incorrect. However, choice A is mistakenly marked correct due to an error in the question's formulation.

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

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