MA 3972-MA-Book April 11, 2018 16:32
AP Calculus AB Practice Exam 1 351
- Iff(x)=8 sin^3 (x),f′
(
π
3
)
is
(A) 6 (B) 9
(C) 6
√
3 (D) 18
- Given the functionf(x)=x^3 − 3 x^2 + 3 x−1,
which of the following statements is true?
(A) The graph offhas a relative minimum at
x=1.
(B) The graph offhas a relative maximum at
x=1.
(C) The graph of f has a point of inflection
atx=1.
(D) The graph of f has a relative minimum
atx=0.
- If
∫− 8
8
f(x)dx=−10 and
∫− 2
− 8
f(x)dx=4,
what is the value of
∫ 8
− 2 f(x)dx?
(A) − 14 (B) − 6
(C) 6 (D) 8
- What is the slope of the tangent line to the
curve 2x^2 y− 3 xy^2 − 2 =0 at the point(2, 1)?
(A) −
5
4
(B) −
2
5
(C)
2
3
(D)
5
4
- Iff is a piecewise function defined as
f(x)=
{
x^2 for x≤ 2
4 x for x> 2 , which of the
following statements is/are true?
I. lim
h→ 0 −
f( 2 +h)−f( 2 )
h
= 4
II. lim
h→ 0 +
f( 2 +h)−f( 2 )
h
= 4
III. f′( 2 )= 4
(A) None
(B) I only
(C) II only
(D) I, II, and III
- Air is pumped into a spherical balloon at the
rate of 10 cubic centimeters per second. How
fast is the diameter, in centimeters per second,
increasing when the radius is 5 cm?
(The volume of a sphere isV=
4
3
πr^3 .)
(A)
1
10 π
(B)
1
5 π
(C)
1
π
(D) 5π
- lim
h→ 0
sin
(
π
3
+h
)
−sin
(
π
3
)
h
is
(A) 0 (B)
1
2
(C) 1 (D)
√
3
2
- The area of the region bounded by the curves
ofy=−x^2 andy=xis
(A) −
5
6
(B)
1
6
(C)
5
6
(D) 6
22.
∫
4
e^2 x
dx=
(A) −
4
e^2 x
+c (B) −
2
e^2 x
+c
(C)
2
e^2 x
+c (D) 4e^2 x+c
- If f(x)=
2 x
(2x−1)^2
, thenf′(x)=
(A)
2
2 x− 1
(B)
1
2 ( 2 x+ 1 )
(C)
2 x+ 1
( 2 x− 1 )^3
(D)
− 2 ( 2 x+ 1 )
( 2 x− 1 )^3
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