A Function Is Given $U ( x ) = 2 \left( x ^ { 3 } - x \right)$

question 73

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.
$U ( x ) = 2 \left( x ^ { 3 } - x \right)$

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Definitions:

Aluminum Concentrations

The amount or level of aluminum present in a given substance, mixture, or environment.

Null Hypothesis

A hypothesis that assumes no significant difference or effect, serving as a default assumption to be tested against experimental data.

Wilcoxon Signed Rank Test

A non-parametric statistical hypothesis test used to compare two related samples, matched samples, or repeated measurements on a single sample to assess whether their population mean ranks differ.

Test Statistic

In hypothesis testing, the test statistic is a standardized value derived from sample data, used to make a decision about the null hypothesis.