Find the Open Interval(s) on Which the Function $f ( x ) = \cos ^ { 2 } ( 3 x )$

question 31

Multiple Choice

Find the open interval(s) on which the function $f ( x ) = \cos ^ { 2 } ( 3 x )$ is increasing in the interval Round numerical values in your answer to three decimal places.

• A) increasing on: \(( 0,0.524 ) , ( 1.047,1.571 ) , ( 2.094,2.618 ) , ( 3.142,3.665 )\)
• B) increasing on: \(( 1.047,0.524 ) , ( 1.047,1.571 ) , ( 2.094,2.618 ) , ( 3.142,4.189 )\)
• C) increasing on: \(( 0.524,1.047 ) , ( 1.571,2.094 ) , ( 2.618,3.142 ) , ( 3.665,4.189 )\)
• D) increasing on: \(( 0,0.524 ) , ( 1.147,1.571 ) , ( 2.094,2.618 ) , ( 3.242,3.665 )\)
• E) increasing on: \(( 1.047,0.524 ) ( 1.047,1.671 ) , ( 2.094,2.618 ) , ( 3.242,4.189 )\)

Calculate the future value of investments using the formula for compound interest.

Determine the present value of future amounts to achieve specific financial goals.

Apply concepts of time value of money in various financial planning scenarios.

Use financial tables or calculators to solve time value of money problems.

---

Definitions:

New Harmony

A utopian community founded by Robert Owen in 1825 in Indiana, USA, intended as an experiment in communal living and social reform.

Modern Times

A period extending from the late 19th century to the present, characterized by rapid advancements in technology, science, and social organization.

Reform Movements

Organized efforts aimed at changing certain societal norms, laws, or practices for improvement.

Protestant Morality

A set of values emphasizing hard work, thrift, and responsibility, often associated with Protestant reformation leaders and influencing societal norms.