Find the Critical Points (If Any) For $f ( x , y ) = \frac { 1 } { x } + \frac { 1 } { y } + x y$

question 63

Essay

Find the critical points (if any) for $f ( x , y ) = \frac { 1 } { x } + \frac { 1 } { y } + x y$ and determine if each is a local extreme value or a saddle point.

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Definitions:

Trait Approach

A theory of leadership that suggests certain inherent personality traits and characteristics contribute to effective leadership.

Behavior Approach

A focus on observable behaviors and external stimuli in understanding human actions, rather than internal thoughts and feelings.

Confidence

A belief in one's abilities, qualities, and judgement.

Optimism

A mental attitude characterized by hope and confidence in the future or the success of something, often leading to a more positive outlook and resilience to challenges.