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Find All Relative Extrema of the Function f(x)=4x2+2f ( x ) = \frac { 4 } { x ^ { 2 } + 2 }

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Find all relative extrema of the function f(x) =4x2+2f ( x ) = \frac { 4 } { x ^ { 2 } + 2 } . Use the Second-Derivative Test when applicable.


Definitions:

Too Cheerful

An overly positive emotional state that may be perceived as insincere or inappropriate in certain contexts or situations.

Internal Locus

A psychological concept referring to individuals who believe they have control over their life events and outcomes, as opposed to external forces.

External Locus

The belief that one's life events are largely controlled by external forces or fate rather than one's own efforts.

Hypothalamus

A small region of the brain's base that controls vital functions such as temperature regulation, thirst, hunger, sleep, and emotional activity.

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