MA 3972-MA-Book April 11, 2018 16:32
352 STEP 5. Build Your Test-Taking Confidence
- Letf andgbe differentiable functions such
thatf−^1 (x)=g(x) for allx. The table below
shows selected values of f(x) and f′(x). What
is the value ofg′(2)?
x 2 4
f(x) 6 2
f′(x) − 5 − 3
(A) − 5 (B) − 3
(C) −
1
3
(D) 2
2
3
1
y
x
- The figure above shows the slope field for
which of the following differential equations?
(A)
dy
dx
=x− 1 (B)
dy
dx
=y− 1
(C)
dy
dx
=y+ 1 (D)
dy
dx
=xy
- Letf be a continuous and twice differentiable
function andf′′(x)>0 for allxin the
interval [4, 5]. Some of the values offare
shown in the table below.
x 4.5 4.6 4.7 4.8
f(x) 10.0 10.2 10.8 11.9
Which of the following is true aboutf′(4.6)?
(A) f′(4.6)< 2
(B) f′(4.6)> 6
(C) 0. 2 < f′(4.6)< 0. 6
(D) 2<f′(4.6)< 6
1
2
f
y
x
- The graph of a functionf is shown in the
figure above. The graph of fconsists of two
line segments, andfis continuous on the
interval[−3, 3].Ifg(x)=
∫x
0
f(t)dt, then
g(− 3 )is
(A) −
5
2
(B) 1
(C)
3
2
(D)
5
2
- The solution to the differential equation
dy
dx
= 3 x^2 ywherey(0)=eis
(A) y=
1
3 x^2
(B) y=e^3 x
(C) y=−e(3x+1) (D) y=e(3x+1)
- The graph of a continuous functiony= f(x)
passes through the point (e, 4) and
dy
dx
=
3
x
.
Which of the following is the functionf(x)?
(A) y=3lnx+e (B) y=3lnx+ 1
(C) y=lnx+ 4 (D) y=ex+ 4
- The definite integral
∫ 3
0
(x^2 +1)dxis
equivalent to which of the following limits?
(A) lim
x→∞
∑n
k= 1
(
1
n
)(
k
n
) 2
(B) lim
n→∞
∑n
k= 1
3
n
((
k
n
) 2
+ 1
)
(C) lim
n→∞
∑n
k= 1
3
n
(
3 k
n
) 2
(D) lim
n→∞
∑n
k= 1
3
n
((
3 k
n
) 2
+ 1
)
STOP. AP Calculus AB Practice Exam 1, Section I Part A.
