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: $( 1.047,0.524 ) ( 1.047,1.671 ) , ( 2.094,2.618 ) , ( 3.242,4.189 )$

Question

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: $( 1.047,0.524 ) ( 1.047,1.671 ) , ( 2.094,2.618 ) , ( 3.242,4.189 )$

Quizplus · Accepted Answer

Explanation:The derivative of $f ( x ) = \cos ^ { 2 } ( 3 x )$ is $f'(x) = -6 \sin ( 3 x ) \cos ( 3 x ) = -3 \sin ( 6 x )$. So, $f(x)$ is increasing on the intervals where $f'(x) > 0$, which are the intervals where $\sin ( 6 x ) < 0$. These intervals are $( 0,0.524 ) , ( 1.047,1.571 ) , ( 2.094,2.618 ) , ( 3.142,3.665 )$.

Find the Open Interval(s) on Which the Function f(x)=cos⁡2(3x)f ( x ) = \cos ^ { 2 } ( 3 x )f(x)=cos2(3x)

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