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:

Adjusted Coefficient

A statistical measure modified to account for various factors or variables, improving its accuracy or relevance.

Partial-regression Coefficient

A measure indicating the change in the dependent variable for a one-unit change in an independent variable while holding other variables constant.

Multiple Determination

A statistical measure that indicates how well data fit a statistical model – often denoted as R-squared in the context of multiple regression analysis.

Multiple Correlation

A measure that represents the strength and direction of a linear relationship between one dependent variable and two or more independent variables.