A Function Is Given $U ( x ) = 4 \left( x ^ { 3 } - x \right)$

question 49

Essay

A function is given. (a) Find all the local maximum and minimum values of the function and the value of x at which each occurs
b) Find the intervals on which the function is increasing and on which the function is decreasing. State each answer correct to two decimal places. $U ( x ) = 4 \left( x ^ { 3 } - x \right)$

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Definitions:

Facial Feedback Hypothesis

The idea that sensory feedback from facial expressions can affect emotional states, suggesting that expressions not only reflect emotions but can influence them.

Circumplex Model

A model that organizes various psychological concepts, such as emotions or personality traits, along two or more dimensions in a circular array.

Differential Emotions Theory

A theory that categorizes emotions into fundamental and discrete categories, each associated with specific physiological patterns and behavioral expressions.

Universal Emotions

Basic emotions that are experienced by all humans across different cultures and include happiness, sadness, anger, fear, surprise, and disgust.