The largest set on which the function $f ( x ) = 3 \sin x$ on $[ 0,2 \pi ]$ is increasing is

A) $\left( 0 , \frac { \pi } { 2 } \right)$
B) $\left( \frac { \pi } { 2 } , \pi \right)$
C) $\left( \pi , \frac { 3 \pi } { 2 } \right)$
D) $\left( 0 , \frac { \pi } { 2 } \right) \cup \left( \frac { 3 \pi } { 2 } , 2 \pi \right)$
E) $( 0,2 \pi )$

Question

The largest set on which the function $f ( x ) = 3 \sin x$ on $[ 0,2 \pi ]$ is increasing is

A) $\left( 0 , \frac { \pi } { 2 } \right)$
B) $\left( \frac { \pi } { 2 } , \pi \right)$
C) $\left( \pi , \frac { 3 \pi } { 2 } \right)$
D) $\left( 0 , \frac { \pi } { 2 } \right) \cup \left( \frac { 3 \pi } { 2 } , 2 \pi \right)$
E) $( 0,2 \pi )$

Quizplus · Accepted Answer

The function $f(x) = 3\sin x$ is increasing where its derivative, $f'(x) = 3\cos x$, is positive. This occurs in the intervals $\left(0, \frac{\pi}{2}\right)$ and $\left(\frac{3\pi}{2}, 2\pi\right)$, making option D the correct answer.

The Largest Set on Which the Function f(x)=3sin⁡xf ( x ) = 3 \sin xf(x)=3sinx

The Largest Set on Which the Function $f ( x ) = 3 \sin x$