Find the Interval on Which $f ( x ) = x - 2 \sin x , 0 \leq x \leq 2 \pi$

Find the interval on which $f ( x ) = x - 2 \sin x , 0 \leq x \leq 2 \pi$ is increasing.

A) $\left[ \frac { \pi } { 3 } , \frac { 5 \pi } { 3 } \right]$

B) $\left[ 0 , \frac { \pi } { 3 } \right]$
C) $\left[ \frac { 5 \pi } { 3 } , 2 \pi \right]$
D) $\left[ 0 , \frac { \pi } { 2 } \right]$
E) $\left[ \frac { \pi } { 2 } , \frac { 3 \pi } { 2 } \right]$
F) $\left[ \frac { 3 \pi } { 2 } , 2 \pi \right]$

G) $[ 0 , \pi ]$

H) $[ \pi , 2 \pi ]$

Correct Answer:

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