AP Calculus BC Quiz
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ANALYTICAL APPLICATIONS OF DIFFERENTIATION
Question 1
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Suppose
b
′
(
3
)
=
0
b'(3)=0
b
′
(
3
)
=
0
and
b
′
′
(
3
)
=
−
1
5
b''(3)=-\tfrac{1}{5}
b
′′
(
3
)
=
−
5
1
; classify the critical point at
x
=
3
x=3
x
=
3
.
A
Neither;
b
′
′
(
3
)
<
0
b''(3)<0
b
′′
(
3
)
<
0
implies concave up
B
Local minimum at
x
=
3
x=3
x
=
3
C
Local maximum at
x
=
3
x=3
x
=
3
D
Neither; the test is inconclusive because
b
′
(
3
)
=
0
b'(3)=0
b
′
(
3
)
=
0
E
Cannot be determined without checking
b
′
′
(
x
)
b''(x)
b
′′
(
x
)
near
3
3
3
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