Name:
Date:
Block:
Midterm Exam Review Sheet 3
Multiple Choice – Non Calculator
1. The graph of y = 3x2 – x3 has a relative maximum at
(a)
(b)
(c)
(d)
(e)
2.
(0,0) only
(1,2) only
(2,4) only
(4, −16) only
(0,0) and (2,4)
108 x5  106 x 4  104 x 2
lim
9 6
7 5
5 3
x  10 x  10 x  10 x
(a) 0
(b) 1
(c) −1
(d) 1/10
3. The figure to the right shows the graph of the velocity of
a moving object as a function of time. At which of the
marked points is the speed the greatest?
(a) A
(b) B
(c) C
(d) D
(e) E
4. What are all values of x for which the graph of y =
2
is concave downward?
4x
(a) There are no values of x.
(b) x < 4
(c) x > – 4
(d) x < – 4
(e) x > 4
5. The equation of the tangent line to the curve
(a)
(b)
(c)
(d)
(e)
5y – 12x = −120
5x – 12y = 119
5x – 12y = 169
12x + 5y = 0
12x + 5y = 169
x2 + y2 = 169 at the point (5, −12) is
(e) −1/10
6. If the graph of f ( x)  2 x 2 
(a)
(b)
(c)
(d)
(e)
k
x
has a point of inflection at x  1 , then the value of k is
−2
−1
0
1
2
7. Piecewise functions f and g are shown to the right.
If h(x) = f ( x) ● g ( x) , then h  3 
8
3
1
(b) 
3
(a) 
(c) 0
2
3
8
(e)
3
(d)
1 t
8. A particle moves along the x-axis in such a way that its position at time (t) is given by x(t ) 
.
1 t
What is the acceleration of the particle at time t = 0?
3
(a) −4
(b) −2
(c) 
(d) 2
(e) 4
5
9. If
d2y
dy
2 2
,
then
=
x y
dx 2
dx
(a) 2xy 2
(b) 4x3 y 3
(c) 2 x  2 x 2 y 3
(d) 2 x 2 y  2 xy 2
(e) 2 x 4 y 3  2 xy 2
1 
10. The average rate of change of the function f ( x)  cos  x  on the closed interval [−4, 0] is
2 
1
(a) − sin(2)
2
6
11. If
x
2
(b) −
1
sin(2)
4
(c)
1  cos(2)
4
(d)
1  cos(2)
4
(e)
1  sin(2)
4
 2 x  2  dx is approximated by three inscribed rectangles of equal width on the x-axis, then the
0
approximation is
(a) 24
(b) 26
(c) 28
(d) 48
(e) 76
Name:
Date:
Block:
Midterm Exam Review Sheet 4
Multiple Choice – Calculator Active
NOTE: The exact numerical value of the correct answer may not always appear among the choices given.
When this happens, select from among the choices the number that best approximates the exact
numerical value.
12. Let f be the function given by f(x) = tan x and let g be the function given by g(x) = x2. At what value
of x in the interval 0 ≤ x ≤  do the graphs of f and g have parallel tangent lines?
(a) 0
(b) 0.660
(c) 2.083
(d) 2.194
(e) 2.207
1
for t  0 . For what value of t is f   t  equal to the average rate of change of f on the
t
closed interval [a, b]?
13. Let f (t ) 
(a)  ab
(d)
1
ab
(b)
ab
(e)
1
2
1 1
  
b a
(c)  1
ab
14. The figure above shows a road running in the shape of a parabola from the bottom of a hill at A to
point B. At B, it changes to a line and continues to on to C. The equation of the road is
ax 2 ,
From A to B
R( x)  
bx  c, From B to C
B is 1,000 feet from A and 100 feet higher. Since the road is smooth, R  x  is continuous. What is the
value of b?
(a) 0.2
(b) 0.02
(c) 0.002
(d) 0.0002
(e) 0.00002
15. The figure above shows the graph of the derivative of a function f. How many points of inflection
does f have in the interval shown?
(a) None
(b) One
(c) Two
(d) Three
(e) Four
16. The amount A  t  of a certain item produced in a factory is given by
A(t) = 4000 + 48(t – 3) – 4(t – 3)3
where t is the number of hours of production since the beginning of the workday at 8:00 a.m. At what
time is the rate of the production increasing most rapidly?
(a)
(b)
(c)
(d)
(e)
8:00 am
10:00 am
11:00 am
12:00 noon
1:00 pm
17. At how many points on the curve y  4 x5  3x4  15x2  6 will the line tangent to the curve pass
through the origin?
(a)
(b)
(c)
(d)
(e)
One
Two
Three
Four
Five
18. The graph of the derivative of a twice differentiable function is shown below.
If f (1) = −2, which of the following must be true?
(a) f (2) < f ′(2) < f ′′(2)
(b) f ′′(2) < f ′(2) < f (2)
(c) f ′(2) < f (2) < f ′′(2)
(d) f (2) < f ′′(2) < f ′(2)
(e) f ′ (2) < f ′′(2) < f (2)
19. The function f  x   tan  3x  has a zero in the interval [0, 1.4]. The derivative at this point is
(a) 0.411
(b) 1.042
(c) 3.451
(d) 3.763
(e) undefined
20. Let f be a function that is everywhere differentiable. The value of f   x  is given for several values of
x in the table below.
x
−10
−5
0
5
10
f  x
−2
−1
0
1
2
If f ′(x) is always increasing, which statement about f (x) must be true?
(a)
(b)
(c)
(d)
(e)
f (x)
f (x)
f (x)
f (x)
f (x)
has a relative min at x = 0.
is concave down for all x.
has a point of inflection at (0, f (0))
passes through the origin
is an odd function
21. The table below gives the values of a differentiable function f. what is the approximate value of f   4  ?
(a) 0.00234
x
f (x)
(b) 0.289
(c) 0.427
(d) 2.340
(e) f   4  cannot be approximated from the information given.
3.99800
3.99900
4.00000
4.00100
4.00200
1.15315
1.15548
1.15782
1.16016
1.16250
22. Which graph best represents the position of a particle, s(t), as a function of time, if the particle’s velocity
and acceleration are both positive?
23.
(a) I only
(b) II only
(c) I and II only
(d) I and III only
(e) II and III only