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:

Moral Standards

Principles that govern behavior, distinguishing between what is right and wrong based on cultural, religious, philosophical, or societal norms.

Sojourner Truth

An African American abolitionist and women's rights activist who famously delivered the "Ain't I a Woman?" speech in 1851.

Women's Rights Movement

A social and political movement aimed at securing and expanding women's rights and equality in society.

Seneca Falls Convention

A pivotal gathering in 1848 that marked the beginning of the women's rights movement in the United States.