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

---

Definitions:

Demand

Prospective customers’ desire for the goods and services available.

Competitor Prices

Refers to the pricing strategies and rates set by companies competing in the same market or industry.

Facial Expression

The movement or position of the face that conveys the emotional state of the individual, including expressions of happiness, sadness, anger, surprise, fear, and disgust.

Messages

Pieces of communication or information conveyed from one person, group, or place to another.