Download Semester Exam Review Part 1 No Calculators

Semester Exam Review
Part 1 No Calculators
1. For the graph shown, at which point is it true that
AA
d
2 < 0 and
dx
dx
>
o?
D.D
C.C
B.B
--t
d2
2. Line L is normal to the curve defmed by 2xy2 - 3y = 18 at the point
E.E
(3,2). The slope of the line L
is?
21
A­
8
32
B.­
3
10
C.-­
21
3. Find the value ofx at which the graph of y
8
21
8
D.21
E.-­
=! + ~ has a point of inflection.
X
C.
4
D.6
C.
1
D. - ­
5. Let y be a differentiable function with dy >
0
A.2
..
4.Fmd
hm
3x+ 2x
3
2
2
3
B.­
2
dx
true that
d 2
d
- y = 8-lny?
dx
A I only
f( x) =
A-..J3rt
7. Let
1t
A.3
8
x-003x -4x +2x
2
A­
3
6. Let
E.
B. II only
cost 37tX
2
) Find
Find
1
B.5
for all x. For which of the following values ofy is it
II. Y = 2
III. Y = 4
C. III only
D. I and II
E. II and III
C.O
..J31t
D.---
E. -1t
1
D. 2-13
E. undefined
f'G)
B. ..J31t
f(x) = tan- 1(x).
3
4
E. - ­
1
y=2
I.
dx
1
2
2
1'(2)
1
2
C.-
Semester Exam Review
Part 1 No Calculators
2
1. For the graph shown, at which point is it true that dy < 0 and d ;, >
dx
B.B
A.A
C.C
dx
O?
D.D
E.E
2. Line L is normal to the curve defmed by 2xy2 - 3y = 18 at the point (3,2). The slope of the line L
is?
21
8
32
3
10
C.-­
21
B.­
A. -
8
21
8
D.21
E.-­
3. Find the value of x at which the graph of y =
.!.. + -J; has a point of inflection.
A.2
4
C.
x
D.6
E.
8
2
l'1m
3x+ 2x
4. Fm
3
2
x-+oo3x -4x +2x
. d
2
3
3
2
B.­
A.-
C. 1
5. Let y be a differentiable function with dy >
dx
true that -
d
dx
A. I only
6. Let
y
2
=
d
8-In y?
B. II only
i( x) = cost 3m2 ).
Find
n
A.­
3
/(x) = tan-I (x).
Find
1
B.­
5
0 for all x. For which of the following values ofy is it
II. Y = 2
III. Y = 4
C. III only
D. I and II
E. II and III
C.O
D.---'
f'G)
A.--J3n
7. Let
E. - ­
1
y=­
2
I.
dx
3
4
1
2
D. - -
-J3n
2
E. -
n
/'(2)
1
C.­
2
1
D.
2-J3
E. undefined
8. The graph of a function
y = f( x) is shown above. Which of the following are true for the function
f(x)?
I.
f'(2) is defmed
II.
lim f(x) = linl f(x)
x-2+
x-2­
f(x)<O forallxon (-1,2)
III.
A. I only
~
I
D. II and III
C.IIIonly
B. II only
c
E. all three
3
9. Let
f(x) = eX - 2x 2 - 4x + 5. Then f has a local minimum at x =?
A.-2
B.
2 2
--c.3
£.2
D.l
3
a( t) = 12t -10.
10. The acceleration of a particle moving along the x-axis is
At t = 0, the velocity is
3. At t = 1, the position is x = 4. Find the position at t = 2.
A.2
D.6
C.5
B.4
3x
11. Find an equation of the line tangent to the graph of y =
A.5x+y=18
B.5x-y=12
(x+ h)2 _x 2
12. Letg(x) = lim
h
h-D
A.
x =1
13. Let
B.
at x = 3.
2
x
E. 7
-6
C.5x+3y=24
D.x-5y=-12
E.
x+ y=6
E.
x=5
. For what value ofx does g(x) = 2?
x=2
C.
x=3
D.
x=4
f be a differentiable function of x that satisfies f (1) = 7 and f ( 4 ) = 3. Which of the
following conditions would guarantee that the tangent line at x =
c is parallel to the secant line joining
(1,f(I)) to (1,f(4))?
A.
f(c)
=
~
B.
f(c)=5
C.
f'(c)
=-~
4
D.f'(c)=_4
3
E.
f'(c) = 4
3
14. Let f(x) = j3 -12x. Which statement about this function is false?
A. The function has one inflection point.
B. The function is concave up for x > 0
C. The function has two relative extrema
D. The function is incr~asing for values of x on (-2,2)
E. The function has a relative minimum at x = 2
1,
15. Let /( x)be a continuous function that is defined for all real numbers x. If / ( x)
when
x -x-6
= -2- - ­
x -5x+6
x 2 - 5x + 6;11! 0, what is /(3)?
AO
B.l
16. Find the derivative of cos
3
E.5
D.4
C.2
(2x )
2
C.6cos (2x)sin(2x)
2
3
A -sin (2x)
B. 6cos (2x)
2
D. - 3cos (2x)sin(2x)
2
E. - 6cos (2x)sin(2x)
17. Let / be a twice differentiable function whose derivative /'( x) is increasing for all x. Which of
the following must be true for all x?
B. II only
A I only
18. The function
A
/(x»O
II.
/'(x) >0
III.
D. I and II
C. III only
/"(x) >0
E. II and III
/(x) = x 3 - 6x 2 + 9x - 4has a local maximum at
x=O
19. Let
I.
B. x
c. x=2
=1
D.
x=3
E.
x=4
/(x) = g(h(x)), where h(2) = 3, h'(2) = 4,g(3) = 2 and g'(3) = 5. Find /'(2).
A 6
B. 8
C. 15
D.20
E. Not enough info to detennine.
20. The velocity of a particle moving along a straight line is given by
v( t) = 3x2 - 4x.
Find an
expression for acceleration of the particle.
A
3x-4
B. 6x-4
C.
x 3 -4x
E.
21. Find the rate of change of the function y
= x 3 - 4x on the closed interval [0,4]
A8
C.24
B. 12
D.32
3x 2 -4
E.48
Ok, you can use your calculator on the rest of these problems.
22. Let / be a differentiable function that is defined for all real numbers x. Use the table below to
estimate /'(3.5).
A 0.3
x
/(x)
3.3
3.4
3.5
3.6
3.7
3.69
3.96
4.25
4.56
4.89
B. 1.8
c.2.7
D.3.0
E.6.0
23. Let
2
..
.
.
f(x) = 3x - 4, for xt1
. WhIch of the followmg are true statements about this function?
{ 6x-5,
I.
for x > 1
limf(x) exists
II.
limf'(x)
f'(l)
III.
exists
x-I
x-I
B. II only
A None of these
C.IIlonly
E. All three.
D. II and III
24. Two particles are moving along the x-axis. Their positions are given by xl (t)
X2(t) = sin(2t) respectively.
If
al (t) and a2(t) represent the acceleration functions of the
particles, find the numbers of values of t in the closed interval [0,5] for which
AD
B.1
25. The function
f( x) =
AD
= 2t 2 - 5 t - 7 and
C.
2
al (tY= a2(t).
E. 4 or more
D.3
3
eX - x has how many critical points?
c.2
B.1
D.3
E.
4 or more
26. A dog heading due north at a constant speed of 2 meters per second trots past a fire hydrant at t =
0
sec. Another dog heading due east at a constant speed of 3 meters per second trots by the hydrant at
t = 1 sec. At t = 9 sec, the rate of change of the distance between the two dogs is
A 3.2 m/s
B. 3.6 m / s C. 4.0 m / s
D.
4.4 m/s
27. Suppose air is pumped into a balloon at a rate given by
volume of the balloon is
\A
2.7ft 3
29. The graph of y
true?
I.
ft% for
r( t) = (lnt)2
t
sec
t ~ 1 sec. If the
1.3ft 3 at t = 1 sec, what is the volume of the balloon at t = 5 sec.?
B.3.0ft 3
28. Find the approximate value of
A - 4.5
E. 4.8 m/s
c. 303ft 3
x where f(x) = x2 - 3-J x + 2
B. - 2
= f'( x)
D. 3.6ft
c. 0
3
E. 3.9ft
3
has its absolute minimum.
D. 0.5
E. 2.5
is shown. Which of the following statements about the function
f(x)
are
,/
f( x) is decreasing for all x on a and c.
II. The graph of f is concave up for all x between a and c
III
f( x) has a relative minimum at x=a
A I only
B. II only
C. III only
D. I and III
E. All three