1. A) 48xy B) -14                                  C) -28                                 D) 24×2

Solve the problem.
3) The profit from the expenditure of x thousand dollars on advertising is given by                                       3)
P(x) = 930 + 25x – 4×2. Find the marginal profit when the expenditure is x = 9.

1. A) 225 thousand dollars/unit B) 153 thousand dollars/unit
2. C) 930 thousand dollars/unit D) -47 thousand dollars /unit

4) Find C(x) if C'(x) = 5×2 –  7x + 4 and C(6) = 260.                                                                                                4)                                                                                                                                                                                                                             

1. A) C(x) = 5x3 –  7 x2 + 4x + 2                                        B) C(x) =  5 x3 –  7 x2 + 4x – 2

3         2                                                                            3         2

1. C) C(x) = 5x3 –  7 x2 + 4x – 260                                   D) C(x) =  5 x3 –  7 x2 + 4x + 260

3         2                                                                            3         2
 
5) The revenue generated by the sale of x bicycles is given by R(x) = 50.00x –  x2 . Find the marginal
200
5)                   
revenue when x = 600 units.

12. A) $100/unit B) $50.00/unit                    C) $56.00/unit                    D) $44.00/unit

6) The rate at which an assembly line worker’s efficiency E (expressed as a percent) changes with              6)
respect to time t is given by E'(t) = 70 – 6t, where t is the number of hours since the worker’s shift
began.  Assuming that E(1) = 92, find E(t).

1. A) E(t) = 70t – 3t2 + 25 B) E(t) = 70t – 3t2 + 92
2. C) E(t) = 70t – 6t2 + 25 D) E(t) = 70t – 3t2 + 159

Identify the intervals where the function is changing as requested.
7) Increasing                                                                                                                                                               7)

1. A) (-2, -1) 1 (2, Q) B) (-1, Q)                            C) (-2, -1)                           D) (-1, 2)

 
 
Determine the location of each local extremum of the function.
8) f(
 
 
 
 
 
 

Find the equation of the tangent line to the curve when x has the given value.
9) f(x) = 5×2 + x ; x = -4                                                                                                                                              9)                                                                                                                                                                                                                             

1. A) y = x +  1

1. B) y = 13x – 16 C) y = -39x – 80                 D) y = –  4x +  8

20     5
25     5
 
Find the largest open interval where the function is changing as requested.
10) Increasing    f(x) = x2 – 2x + 1                                                                                                                              10)                                                                                                                                                                                                                   A) (-Q, 0)                             B) (0, Q)                              C) (-Q, 1)                            D) (1, Q)
 
 
Find dy/dx by implicit differentiation.
11) 2xy – y2 = 1                                                                                                                                                            11)                                                                                                                                                                                                                               

1. A)   x   

y – x

1. B)   x   

x – y

1. C)   y   

x – y

1. D)   y   

y – x
 
Find the area of the shaded region.
12)                                                                                                                                                                                  12)

1. A) 5

3

1. B) 3 C) 5                                     D)  23

3
 
Use the properties of limits to evaluate the limit if it exists.
13)   lim x    6
   x + 6    (x – 6)2
13)                 

1. A) 0 B) 6                                     C) -6                                   D) Does not exist

14)  lim   x3 + 12x2 – 5x
x  0
14)
5x

1. A) 0 B) Does not exist               C) -1                                   D) 5

 
 
Evaluate.

15)          34  dx                                                                                                                                                              15)                                                                                                                                                                                                                               
x2

1. A) 34x + C B)  34 + C                            C) -34x + C                        D) –  34 + C

x                                                                                          x
 
Find the integral.

16)            19     dy                                                                                                                                                         16)                                                                                                                                                                                                                               
2 + 5y

1. A) 18ln  2 + 5y  + C                                                       B)  19 ln  2 + 5y  + C

5                                                                                       5
 

1. C) 19 ln 2 + 5y + C                                                       D) 18 ln  2 + 5y  + C

 
17)  a   8x – 9x-1  dx                                                                                                                                                  17)                                                                                                                                                                                                                    A) 4×2 – 9 ln  x  + C                                                        B) 4×2 +  9 x-2 + C
2

1. C) 16×2 – 9 ln x + C                                                     D) 16×2 +  9 x-2 + C

2
 

18)              x dx       (7×2 + 3)5

1. A) – 1 (7×2 + 3)-4 + C                                                   B) –  1  (7×2 + 3)-6 + C

18)                 
56
                 -4
14
 7               -6

1. C) – 7 (7×2 + 3)

3
+ C                                                    D) –
(7×2 + 3)     + C
3
 
19)  a 9z    3z2 – 7 dz                                                                                                                                                  19)                                                                                                                                                                                                                    A) z(3z2 – 7)3/2 + C                                                           B) (3z2 – 7)3/2 + C
                    3/2
 1               3/2

1. C) 1 z(3z2 – 7)

2
+ C                                                    D)
(3z2 – 7)      + C
2
 
Find the absolute extremum within the specified domain.
20) Maximum of f(x) = x2 – 4; [-1, 2]                                                                                                                        20)                                                                                                                                                                                                                    A) (-1, 3)                             B) (-2, 0)                             C) (1, -3)                             D) (2, 0)
Assume x and y are functions of t. Evaluate dy/dt.
21) x3 + y3 = 9;  dx = -5, x = 2                                                                                                                                    21)                                                                                                                                                                                                                               
dt

1. A) 20 B)  5

4

1. C) 4

5

1. D) – 20

 
Use the given graph to determine the limit, if it exists.
22)
22)
lim
x  0-
f(x) and  lim
x  0+
f(x).

1. A) -1; 1 B) 1; -1                                C) 1; 1                                 D) -1; -1

 
 
Find the derivative of the function.
23) y = (3×2 + 5x + 1)3/2                                                                                                                                               23)                                                                                                                                                                                                                               

1. A) y’ = (6x + 5)(3×2 + 5x + 1)1/2 B) y’ = (3×2 + 5x + 1)1/2

1. C) y’ = 3(3×2 + 5x + 1)1/2                                              D) y’ =  3 (6x + 5)(3×2 + 5x + 1)1/2

2                                                                                       2
 
24) y = ln (3×3 – x2)                                                                                                                                                     24)                                                                                                                                                                                                                               

1. A) 3x – 2  

3×2 – x

1. B) 9x – 2  

3×3 – x

1. C) 9x – 2  

3×2 – x

1. D) 9x – 2

3×2
 
Find the derivative.
25) y = e5x2 + x                                                                                                                                                            25)                                                                                                                                                                                                                    A) 10xe + 1                          B) 10xe2x + 1                      C) 10xex2 + 1                     D) 10xe5x2 + 1
 
 
26) f(x) = 20×1/2 –  1 x20                                                                                                                                               26)                                                                                                                                                                                                                               
2

1. A) 10×1/2 – 10×19 B) 10×1/2 – 10×10              C) 10x-1/2 – 10×19            D) 10x-1/2 – 10×10

Find the general solution of the differential equation.
27)  dy  = x – 2                                                                                                                                                               27)                                                                                                                                                                                                                               
dx

1. A) x2– x + C                      B) x3 – 2x + C                    C) 2×2 – 2 + C                    D)  x2 – 2x + C

2                                                                                                                                    2
 
Evaluate f”(c) at the point.
28) f(x) =  3x – 4 ,  c = 1                                                                                                                                                 28)                                                                                                                                                                                                                               
4x – 3

 
Find the largest open intervals where the function is concave upward.
30) f(x) = x3 – 3×2 – 4x + 5                                                                                                                                          30)                                                                                                                                                                                                                    A) (-Q, 1)                             B) None                              C) (1, Q)                              D) (-Q, 1), (1, Q)