Math 111 FINAL REVIEW Multiple Choice Questions
 4 x2  9 
lim
1.


x  2 x 2  6


A. –infinity
B. infinity
2
 x  x  20 
2. lim 

x 4
 x4 
A. 0
B. 4
C. 5
3. THE DERIVATIVE OF f ( x)  ln(4 x
A.1/(4x3 – x)
B. ln(12x2 -1)
C. 2
D. 4
D. 9
3
 x)
IS…………
C. (12x2 -1)/( 4x3 – x)
D. Does not exist
f ( x)   3x3  5 x  IS…………
6
4. THE DERIVATIVE OF
A. (9𝑥 2 − 5)6
B. 6(3x3 – 5x)5(9x2-5)
5. THE DERIVATIVE OF
A.
𝑒 𝑥 (𝑥−3)
4𝑥 4
𝑒𝑥
C. 6(3x3 – 5x)5
D. 6x5
ex
f ( x)  3 IS (SIMPLIFIED)…………
4x
B. 12𝑥2
1
C. 𝑒 𝑥 4 (𝑥 −4 )
D. 12xex
6. USE THE FIRST DERIVATIVE TEST TO FIND THE INTERVALS WHERE THE FUNCTION IS INCREASING.
f ( x)  x 3  3x 2  9 x  3 .
A. (-infinity, 3)
B. (3, infinity)
C. (-infinity, -3) U (1, infinity) D. (-3,1)
7. FIND THE EQUATION OF THE TANGENT LINE TO
A. y = 3x + 19
B. y = -6x + 14
f ( x)  x3  6 x 2  24 x
C. y = x + 19
AT (1, 19).
D. y = 15x + 4
8. IF R( x)  0.2 x  65 x AND C ( x)  5 x  2000 , USE THE FIRST DERIVATIVE TEST TO FIND WHAT
VALUE OF X GIVES THE MAXIMUM PROFIT.
2
A. 50
B. 100
C. 150
D. 200
9. USE THE SECOND DERIVATIVE TO FIND THE INTERVALS FOR WHICH f(x) IS CONCAVE DOWN.
f ( x)  x 4  2 x 3
A. (-infinity, 0)
B. (0,1)
C. (-infinity, 0)U(1, infinity)
D. (1, infinity)
10. WHAT ARE THE CRITICAL POINTS OF f(x) = (1/3)x3 - (5/2)x2 - 24x?
A. 2, 5
B. -3, 8
C. 3, 8
D. -8, 3
11.
FOR THE GRAPH ABOVE……..
A). f ` (x) > 0 f ``(x) > 0
C) f ` (x) < 0 f ``(x) > 0
D) f ` (x) < 0 f ``(x) < 0
B). f ` (x) > 0
f ``(x) < 0
1
12. IF f(x) = x2 , WHICH IS THE LIMIT DEFINITION OF THE DERIVATIVE?
B. (x+h)2 – x2
A. x2/h
C. limh-> 0((x+h)2 – x2)/h
D. limh-> 0((x+h)2 – x2)/h
13. THE RATE OF ARRESTS FOR DRUG VIOLATIONS IN THE U.S. IS GIVEN BY….
D`(t )  0.3t 2  10.56t  40.31 , WHERE t = 0 IS 1970 AND THE ARREST RATE IS MEASURED IN
THOUSANDS OF ARRESTS
. FIND THE TOTAL NUMBER OF ARRESTS FOR THE FIRST 5 YEARS
YEAR
BEGINNING WITH 1970.
A. 321
14.
B. 86

  x
3
 2x 
  2x
4
4
𝑥
A.
55
3
16.
2
0
2
1
26
3
C. 26
C. 3𝑥 2 − 2 −
−8
𝑥3
1
4
D. 𝑥 4 − 𝑥 2 −
4
𝑥
D. 55
C. ln(13) – ln(7)
B. .25ln(7)
D. .25ln(13) - .25ln(7)
𝑡
∫0 2𝑒 4𝑥 𝑑𝑥 =
A. e4t – 1
18.
4
𝑥
 x 
 2
 dx 
 2x  5 
A. .25 ln(13)
17.
1
4
B. 𝑥 4 − 𝑥 2 − + 𝐶
 x  2  dx 
B.

D. 52613
4 
 dx 
x2 
A. 𝑥 4 − 𝑥 2 − + 𝐶
15.
C. 4031
𝑡
∫3
A. 24
B. 2e4t – 2
6
√𝑥+1
C. .5e4t – .5
D. e4t
𝑑𝑥 =
B. 12√𝑡 + 1 - 24
C. 12√𝑡 + 1
D. 3√𝑡 + 1 - 8
19. IF THE MARGINAL COST IS GIVEN BY MC(x) = 10X + 22, AND THE FIXED COSTS ARE $7,500, FIND C(x).
A. 10x + 22 – 7500
B. 10x + 22 + 7500
C. 5x2 + 22x + 7500
D. 5x2 + 22x - 7500
20. FIND THE AREA BETWEEN f(x) = 2x + 7 and
g(x) = - x2 + 4 ON [ -3, 2].
A.
21
3
B.
65
3
C. 21
D. 65
21. FIND THE DERIVATIVE OF 𝑓(𝑥) =
A. x+3
B. 1
C. (x+3)2
𝑥 2 +6𝑥+9
.
𝑥+3
D. 3
2