Using the Derivative of F(x) Given Below, Determine the Intervals $$f ^ { \prime } ( x ) = x ^ { 1 / 3 } ( x - 7 )$$

question 28

Multiple Choice

Using the derivative of f(x) given below, determine the intervals on which f(x) is increasing or decreasing.
- $$f ^ { \prime } ( x ) = x ^ { 1 / 3 } ( x - 7 )$$

• A) Decreasing on \(( 0,7 )\); increasing on \(( - \infty , 0 ) \cup ( 7 , \infty )\)
• B) Increasing on \(( 0 , \infty )\)
• C) Decreasing on \(( 0,7 )\); increasing on \(( 7 , \infty )\)
• D) Decreasing on \(( - \infty , 0 ) \cup ( 7 , \infty )\); increasing on \(( 0,7 )\)

Evaluate the relationship between societal expectations and individual behavior through concepts such as the self-fulfilling prophecy and the Thomas theorem.

Discern the variability and significance of life stages across cultures and historical periods.

Understand the processes and outcomes of gender role socialization and its effects on individual identities.

Investigate how personal experiences and societal influences interact to shape individuals' responses to their environments.

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Definitions:

Obligated To Obey

Required or bound by law, duty, or moral principle to follow commands or instructions.

Authority

The authority or capacity to direct, make choices, and ensure compliance.

Adolescents

Individuals transitioning from childhood to adulthood, typically between the ages of 10 and 19, experiencing significant physical, psychological, and social changes.

Steepest Decline

describes the fastest decrease or most significant drop in a value or quantity over a specific period.