Name:
Date:
Chapter 3 Test Review
Calculator Not Allowed
Directions: Find all critical points for the following functions. Determine where each of the following
functions is increasing and decreasing. Classify all maximum and minimum values.
1. f ( x)  x 4  3x 2  2
2. f ( x)  2 x3  3x 2  12 x  5
3. f ( x)  ( x  3)2
4. f ( x)  x 
5. f ( x) 
1
x
x2  8
x 1
Directions: Determine where each of the following functions is concave up and down. Find all inflection
points.
6. f ( x)  x3  3x3  4 x  1
7. f ( x)  x 4  6 x 2  2 x  3
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Directions: Given the following derivatives, find the local extrema and inflection points for f(x).
8. f '( x)  x 4  16
9. f '( x)  ( x  5) 2
Directions: Determine whether the Mean Value Theorem applies on the given intervals. If they do, find
the exact value of all c that satisfy the conclusion of the MVT.
10. f ( x)  x 2 on [-2,1]
11. f ( x)  x 2 on [0,3]
12. f ( x)  x3  x 2  2 x on [-1,1]
13. f ( x)  ( x  3)( x  1) on [-1,0]
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Directions: Sketch a graph of each of the following functions. Find the zeros, y-intercept, max/min,
increasing, and decreasing.
14. f ( x)  x3 ( x  4)
-10
15. f ( x)  ( x  2)( x  1)
6
6
4
4
2
2
-5
5
10
-10
-5
5
-2
-2
-4
-4
-6
-6
10
Calculators Allowed
Directions: Sketch a graph of a function with the following characteristics.
16.
x
f'(x)
17.
( , 2)
( 2, 4)
(4, )
Positive
Negative
Positive
( , 3)
x
f(x)
Negative
Positive
6
6
4
4
2
2
-5
5
10
-10
-5
5
-2
-2
-4
-4
-6
-6
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(-1,3)
(3, )
Negative Positive
(-2,1)
(1, )
Negative Positive
( , 2)
x
f’(x)
-10
(-3,-1)
Positive
10
18. A 10 ft ladder leans against the side of a building. If the top of the ladder begins to slide down the
wall at a rate of 2 ft/s, how fast is the bottom of the ladder sliding away from the wall when the ladder is
8 feet from the ground?
19. Oil spills out of a tanker at a rate of 120g/m. The oil spreads in a circle. Determine the rate at which
the radius of the spill is increasing when the radius is 100ft.
20. Sand is dumped such that the shape of the sand pile remains a cone with height equal to the radius.
If the sand is dumped at the constant rate of 20 cubic ft/s, find the rate at which the height is increasing
when the height is 6 ft.
21. You have 1200ft of fencing. What is the largest area you can create?
22. What size squares should be cut out if you have a piece of material that is 15 by 11 and want to
create an open-top box?
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