Using the Derivative of F(x) Given Below, Determine the Intervals $$f ^ { \prime } ( x ) = x ^ { 1 / 3 } ( x - 6 )$$

question 237

Multiple Choice

Using the derivative of f(x) given below, determine the intervals on which f(x) is increasing or decreasing.
- $$f ^ { \prime } ( x ) = x ^ { 1 / 3 } ( x - 6 )$$

• A) Decreasing on \(( - \infty , 0 ) \cup ( 6 , \infty )\); increasing on \(( 0,6 )\)
• B) Decreasing on \(( 0,6 )\); increasing on \(( - \infty , 0 ) \cup ( 6 , \infty )\)
• C) Decreasing on \(( 0,6 )\); increasing on \(( 6 , \infty )\)
• D) Increasing on \(( 0 , \infty )\)

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Definitions:

Fixed-Weight Price Index

A method of calculating inflation or deflation that uses predetermined weights for different categories of goods and services, regardless of their current market importance.

Chain-Weighted System

An inflation measure that adjusts the weights from year to year in calculating a price index, thereby reducing the bias caused by a fixed-price weighting system.

Nominal Gross Domestic Product (GDP)

The market value of all goods and services produced within a country in a given period, measured without adjusting for inflation.

Real GDP

The total value of all goods and services produced by a country in a year, adjusted for inflation, making it a measure of economic output that accounts for changes in the price level.