Determine the Concavity of F(x) = Cos X + Sin $\pi$

Multiple Choice

Determine the concavity of f(x) = cos x + sin x on [0, 2 $\pi$ ] and identify any points of inflection.

A) concave down on [0, 3 $\pi$ /4) (7 $\pi$ /4, 2 $\pi$ ], concave on (3 $\pi$ /4, 7 $\pi$ /4) ; inflection points at x = 3 $\pi$ /4 and
B) concave up on [0, 3 $\pi$ /4) 11ee7b09_453f_4329_ae82_2b7669cf7fd7_TB9661_11 (7 $\pi$ /4, 2 $\pi$ ], concave down on (3 $\pi$ /4, 7 $\pi$ /4) ; inflection points at x = 3 $\pi$ /4 and 11ee77e1_7827_4392_a0f8_c913310a9fb4_TB9661_11
C) concave down on [0, $\pi$ /4) 11ee7b09_453f_4329_ae82_2b7669cf7fd7_TB9661_11 (5 $\pi$ /4, 2 $\pi$ ], concave up on ( $\pi$ /4, 5 $\pi$ /4) ; inflection points at x = $\pi$ /4 and 11ee77e1_7827_4393_a0f8_6530a91cfcbe_TB9661_11
D) concave up on [0, $\pi$ /4) 11ee7b09_453f_4329_ae82_2b7669cf7fd7_TB9661_11 (5 $\pi$ /4, 2 $\pi$ ], concave down on ( $\pi$ /4, 5 $\pi$ /4) ; inflection points at x = $\pi$ /4 and 11ee77e1_7827_6aa4_a0f8_19008de1a10d_TB9661_11
E) concave down on (0, 3 $\pi$ /4) 11ee7b09_453f_4329_ae82_2b7669cf7fd7_TB9661_11 (7 $\pi$ /4, 2 $\pi$ ) , concave up on (3 $\pi$ /4, 7 $\pi$ /4) ; inflection points at x = 3 $\pi$ /4 and 11ee77e1_7827_6aa5_a0f8_a1b06871ebbd_TB9661_11