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 $f ( x ) = - \sin x + \cos x \text { on the interval } ( 0,2 \pi )$ .

A) no inflection points. concave up on $( 0,2 \pi )$
B) concave upward on $\left( 0 , \frac { 1 } { 2 } \pi \right)$ ; concave downward on $\left( \frac { 5 } { 2 } \pi , 2 \pi \right)$ ; inflection point at $\left( 0 , \frac { 1 } { 2 } \pi \right)$
C) no inflection points. concave down on $( 0,2 \pi )$
D) concave downward on $\left( 0 , \frac { 1 } { 2 } \pi \right)$ ; concave upward on $\left( \frac { 5 } { 2 } \pi , 2 \pi \right)$ ; inflection point at $\left( 0 , \frac { 1 } { 2 } \pi \right)$
E) none of the above