Download MAC2233 Survey of Calculus Practice Test #3

MAC2233
Survey of Calculus
Practice Test #3
1) For the function graphed to the right, identify:
a) The Critical Numbers
______________
b) Relative Extrema
______________
c) Points of Inflection
______________
d) Increasing Intervals
______________
e) Decreasing Intervals
______________
f) Concave Upward Intervals
______________
g) Concave Downward Intervals ______________
2) Use the following information to graph the function f(x):
x
y
0
2
4
6
8
10
12
14
16
18
13
8
10
f ′ (x):
-
| + |
2
4
-
| + | + |
6
8
10
f ′′ (x): + | + |
-
|
6
-
|
12
-
-
| + | + | + | + |
12
14
16
18
20
| + | + | + |
14
16
18
20
Und.
10
13
9
1
8
20
2
4
-
|
8
-
|
10
lim f ( x) = −∞ ; d.n.e.
x→ 6
3) For the function,
4)
f(x) = x3 − 6x2 − 15x + 3 ,
identify:
a) The Critical Numbers
______________________
b) Relative Extrema
______________________
c) Points of Inflection
______________________
d) Increasing Intervals
______________________
e) Decreasing Intervals
______________________
f) Concave Upward
______________________
g) Concave Downward
______________________
An open box is to be made from a 9 in. by 12 in. rectangular piece of material, by cutting equal
squares from each corner and turning up the sides. Find the volume of the largest box that
can be made in this manner.
5)
A dog owner has 300 ft of fencing to use for a rectangular dog run. If he puts the run next to
the garage he only needs to use the wire for three sides. What dimensions will yield the
maximum area?
6)
Given the re venue function R(x) = 200x - 10x and the cost function C(x) = 100 + 40x ,
find the number of units to produce in order to maximize the profit.
2
7)
The demand for a certain product is given by the model p =
25
x
The fixed costs are $205 and the cost per unit is $0.50
Find the price that will maximize the profits.
8)
The diameter of a sphere is measured to be 12 inches, correct to within the nearest tenth of
an inch ( 0.1 inches). How far off could the calculation of the volume be?
What is the relative error in the volume? [Hint: Use Marginal Analysis (Differentials)]