AP Calculus BC Quiz
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ANALYTICAL APPLICATIONS OF DIFFERENTIATION
Question 1
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For all real
x
x
x
,
f
′
′
(
x
)
=
2
sin
x
f''(x)=2\sin x
f
′′
(
x
)
=
2
sin
x
; on which intervals is
f
f
f
concave up and concave down on
[
0
,
2
π
]
[0,2\pi]
[
0
,
2
π
]
?
A
Concave up on
(
0
,
π
)
(0,\pi)
(
0
,
π
)
; concave down on
(
π
,
2
π
)
(\pi,2\pi)
(
π
,
2
π
)
B
Concave up on
(
π
,
2
π
)
(\pi,2\pi)
(
π
,
2
π
)
; concave down on
(
0
,
π
)
(0,\pi)
(
0
,
π
)
C
Concave up on
(
0
,
π
2
)
∪
(
3
π
2
,
2
π
)
(0,\tfrac{\pi}{2})\cup(\tfrac{3\pi}{2},2\pi)
(
0
,
2
π
)
∪
(
2
3
π
,
2
π
)
; concave down on
(
π
2
,
3
π
2
)
(\tfrac{\pi}{2},\tfrac{3\pi}{2})
(
2
π
,
2
3
π
)
D
Concave up on
(
0
,
2
π
)
(0,2\pi)
(
0
,
2
π
)
; concave down on no interval
E
Concave up on no interval; concave down on
(
0
,
2
π
)
(0,2\pi)
(
0
,
2
π
)
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