Find the Local Maximum and Minimum Values and Saddle Points $f ( x , y ) = x ^ { 3 } - 3 x y - y ^ { 3 }$

question 102

Essay

Find the local maximum and minimum values and saddle points of the function $f ( x , y ) = x ^ { 3 } - 3 x y - y ^ { 3 }$ .

---

Definitions:

Optimistic

Having a hopeful and confident attitude towards the future or the successful outcome of something.

Pessimistic

Having a tendency to see the worst aspect of things or believe that the worst will happen; a lack of hope or confidence in the future.

Egocentrically Introverted

A personality trait characterized by a focus on one's own thoughts and feelings rather than on external stimuli or the perspectives of others.

Disinhibition

The reduction of restraint or inhibition which can lead to an increase in spontaneous or impulsive behaviors, often seen in social or psychological contexts.