Find the Points of Inflection and Discuss the Concavity of the Function

Multiple Choice

Find the points of inflection and discuss the concavity of the function $f ( x ) = - 8 x - 2 \cos x$ on the interval $[ 0,2 \pi ]$

A) concave down on $( 0,2 \pi )$ ; no points of inflection
B) concave downward on $\left( \frac { \pi } { 2 } , \frac { 3 \pi } { 2 } \right) ;$ concave upward on $\left( 0 , \frac { \pi } { 2 } \right) , \left( \frac { 3 \pi } { 2 } , 2 \pi \right)$ ; inflection points at $x = \frac { \pi } { 2 }$ and $x = \frac { 3 \pi } { 2 }$
C) concave upward on $\left( \frac { \pi } { 2 } , \frac { 3 \pi } { 2 } \right) ;$ concave downward on $\left( 0 , \frac { \pi } { 2 } \right) , \left( \frac { 3 \pi } { 2 } , 2 \pi \right)$ inflection points at $x = \frac { \pi } { 2 }$ and $x = \frac { 3 \pi } { 2 }$
D) concave up on $( 0,2 \pi )$ ; no points of inflection
E) none of the above