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

question 80

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 all answers correct to two decimal places.
$U ( x ) = 4 \left( x ^ { 3 } - x \right)$

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Definitions:

Semantic Memories

Refers to a type of long-term memory involving the capacity to recall words, concepts, and facts without related to personal experience.

Episodic Memories

Memories of specific events or episodes, including the contexts and emotions associated with them.

Procedural Memory

A type of long-term memory that involves the recall of how to perform tasks or skills.

Implicit Memory

A type of long-term memory that enables us to perform tasks without conscious awareness of these previous experiences.