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Calculus 3rd Quarter Exam Review Name___________________
1. Find all intervals on which the graph of the function is concave upward: ( )
x 1 f x x 4
A) ( −∞ ∞, ) B) ( −∞ −, 4 ) C) ( −4, ∞ ) D) ( −∞, 4 ) E) ( 4, ∞)
2. Find all intervals on which the graph of the function is concave downward: ( )
2
x f x
x 2
A) ( −∞ ∞, ) B) ( −∞ −, 2 ) ∪ −( 2, 4 ) C) ( −2, ∞ ) D) ( −∞, 4 ) E) ( 4, ∞)
- Which of the following are the equations of all horizontal and vertical asymptotes for the function
2
3
x 3x f x x 9x
Horizontal asymptote Vertical asymptote(s)
A) y = 0 x = 0 and x = 3
B) y = 0 x = 0, x = − 3, and x = 3
C) y = 0 x = 3
D) y = 1 x = 0 and x = 3
E) y = 1 x = 3
- Which of the following are the equations of all oblique and vertical asymptotes for the function
2 x 3x 1 f x x 2
Oblique asymptote Vertical asymptote(s)
A) y = x − 1 x = 2
B) y = x + 5 x = − 2
C) y = x − 1 none
D) y = x + 1 x = − 2
E) y = x + 5 x = 2
- Determine which of the following is true given the following information:
f ( 2 ) = 10, f ′^ ( 2 ) = 0, and f ′′( 2 )<0.
A) ( 2,10 )is a relative maximum B) ( 2,10 )is a relative minimum C) ( 2, 0) is a relative max
D) not enough information E) no relative extrema
- Find the length and width of a rectangle that has an area of 36 square feet and a minimum perimeter.
A) 4 ft by 9 ft B) 3 ft by 12 ft C) 6 ft by 6 ft
D) 1 ft by 36 ft E) 4ft by 12ft
- The product of two positive numbers is 288. Minimize the sum of the first number and two times the
second number.
A) 144, 72 B) 12, 24 C) 12 2, 12 2 D) 16, 18 E) 6, 48
- A rancher has 180 feet of fencing with which to enclose two adjacent rectangular corrals. Which of
the following dimensions should be used so that the enclosed area will be a maximum?
A) 45’ by 30’ B) 40’ by 30’ C) 50’ by 15’ D) 60’ by 20’ E) 1’ by 180’
9. State why the Mean Value Theorem does not apply to the function ( )
3 f x = 2 x on the interval (^) [ −1,1]
A) f is not continuous at x = 0 B) f is not differentiable at x = 0 C) f is not continuous at x = 1
D) f is not differentiable at x = 1 E) Mean Value Theorem does apply
10. State why the Mean Value Theorem does not apply to the function ( )
2 f x = x^3 on the interval [ 0,1]^.
A) f is not continuous at x = 0 B) f is not differentiable at x = 0 C) f is not continuous at x = 1
D) f is not differentiable at x = 1 E) Mean Value Theorem does apply
16. Evaluate ( )
2 sec x − sin x −2x dx
A) (^) tan x − cos x − x + C B)
2 tan x − cos x − x + C C)^
2 tan x − cos x − 2x +C
D) tan x + cos x − x + C E)
2 tan x + cos x − x +C
17. Evaluate ( )
2 tan x +1 dx
A) sec x + x + C B) sec x tan x + C C) tan x + C D)
2 sec x + C E) sec x +C
18. Evaluate ( )
1 2
0
x − 2x +1 dx
A) 0 B)
C) 1 D) 2 E) 7
- Evaluate
2
1 2
x dx x
A) 1 B) 2 C) 4 D) 5 E) 10
- Evaluate
6
2
3 dx
A) 0 B) 3 C) 12 D) 18 E) 24
- Which of the following definite integrals represents the area of the shaded region?
A) ( )
6
0
6 −2x dx
B)
(^9 2 )
0
3x x dx 3
C) ( )
9 2
0
6x −x dx
D)
(^6 2 )
0
3x x dx 3
E) ( )
6 2
0
6x −x dx
2 (^9) y = 6x −x
6
- Which of the following definite integrals represents the area of the shaded region?
A) ( )
7
1
2x + 1 dx
B) ( )
7 2
1
x +x dx
C) ( )
3
0
2x + 1 dx
D) ( )
7 2
1
x +x dx
E)
3
0
2 dx
- Integrate:
3x
2
x
3
dx
A)
3
2 x + 1 + C B) ( )
3 (^3 2 ) x 1 C 2
+ + C)
3 x + 1 +C
D)
x 1 C 2
+ + E)^ ( )
x 1 C 3
dy (^2) x cos 3x , then y dx
A) ( )
sin 3x C 6
+ B) ( )
sin 3x C 6
− + C) ( )
cos 3x C 6
D) ( )
2
sin 3x + C E) ( )
2 cos 3x +C
- If
2 x f (x) , 2
′ = where f (0) = 0 then 3f (4)=
A) 0 B) 3 C) 12 D) 24 E) 32
y = 2x + 1 7
3
1
4
Answers to Calculus 3
rd quarter exam review:
1. E 2. B 3. C 4. D 5. A 6. C 7. B
8. A 9. B 10. E 11. B 12. B 13. C 14. D
15. A 16. E 17. C 18. B 19. A 20. C 21. E
22. C 23. A 24. A 25. E 26. C 27. D 28. A
29. B 30. E 31. D
