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Worksheetsfunction analysis/ optimization
Total questions: 23
Worksheet time: 54mins
Name
Class
Date
1.
Given a function, f(x), if f'(x)<0 over a certain interval, then f(x) is ____________ over that interval.
a)
decreasing
b)
increasing
c)
concave up
d)
concave down
2.
Given a function, f(x), if f'(x)>0 over a certain interval, then f(x) is __________ over that interval.
a)
increasing
b)
decreasing
c)
concave up
d)
concave down
3.
Given a function g(x), if g''(x)=0 for a certain value of x, then g(x) has _________ at x.
a)
an inflection point
b)
a maximum
c)
a minimum
d)
a critical point
4.
Given a function g(x), if g'(x)=0 at a certain value of x, then g(x) has _____________ at x.
a)
an inflection point
b)
a critical point
c)
a minimum
d)
a maximum
5.
For a function f(x), f''(4)=0 indicates that x=4 is _____________.
a)
an inflection point
b)
a critical point
c)
a relative maximum
d)
a relative minimum
6.
For a function g(x), g'(-2)=0 indicates that x=-2 is ________________.
a)
an inflection point
b)
a critical point
c)
a relative maximum
d)
a relative minimum
7.
The concavity of a function is described by its _______________.
a)
first derivative
b)
second derivative
c)
third derivative
d)
expression
8.
The slope of a function is described by its ____________.
a)
first derivative
b)
second derivative
c)
third derivative
d)
expression
9.
For a function g(x), g''(3)=-8 indicates that g(x) is ____________ at x=3.
a)
increasing
b)
decreasing
c)
concave up
d)
concave down
10.
f(x) is pictured. Over what interval is f(x) apparently decreasing?
a)
(infinity, 0)
b)
(-infinity, 0)
c)
(-infinity, infinity)
d)
(0, infinity)
11.
f(x) is pictured. Over which interval is f(x) apparently concave up?
a)
(0, infinity)
b)
(-infinity, infinity)
c)
(-infinity, 0)
d)
nowhere
12.
g(x) is pictured. Over which interval(s) is g(x) apparently increasing.
a)
(-infinity, 4)
(4, infinity)
(4, infinity)
b)
(-infinity, 1)
(1, infinity)
(1, infinity)
c)
(4, infinity)
d)
nowhere
13.
We need to enclose a field with a fence. We have 500 feet of fencing material and a building is on one side of the field so we won't need any fencing on that side. Determine the dimensions of the field that will enclose the largest area.
a)
x=250 ft, y=125 ft
b)
x=150 ft, y=200 ft
c)
x=125 ft, y=100 ft
d)
x=200 ft, y=150 ft
14.
We want to construct a box whose base length is 3 times the base width. If the box must have a volume of 50 ft3, determine the dimensions that will minimize the amount of material used.
a)
w=2.027ft, h=4.055ft, l=6.082ft
b)
w=1.488ft, h=3.347ft, l=6.694ft
c)
w=2.231ft, h=3.347ft, l=6.694ft
d)
w=0.485ft, h=2.111ft, l=4.222ft
15.
A rectangular page is to contain 144 sq. inches of print. the margins on each side are 1 inch. Find the dimensions of the page that would use the least paper
a)
16, 16
b)
15,15
c)
14,14
d)
13,13
16.
If y=2x-8, what is the minimum value of the product xy?
a)
-16
b)
-8
c)
-4
d)
2
17.
Having the courage to do the right thing because it is right is called
a)
Morality
b)
Integrity
c)
Honesty
d)
Immorality
18.
Who are your "peers"?
a)
Your parents
b)
People who are your age, like your classmates
c)
Your teachers
d)
Your pets
19.
Why do some kids give into peer pressure?
a)
Because they want to be liked, to fit in.
b)
Because they worry that other kids might make fun of them if they don't go along with the group
c)
Because they are curious to try something new that others are doing.
d)
All of the above
20.
Peer Pressure can be...
a)
Positive
b)
Negative
c)
Neither
d)
Postive or Negative
21.
A friend encourages you to try out for the basketball team. This is which type of pressure?
a)
Positive Pressure
b)
Negative Pressure
22.
If f '(3) = 0 and f"(3) < 0, then which of the following must be true?**HINT:2nd Derivative Test***
a)
There is a local max at x=3
b)
There is a local min at x = 3
c)
There is an inflection point at x = 3
d)
There is an x-intercept at x = 3
23.
The graph shown is the DERIVATIVE of f. From the derivative's graph, identify the interval graph where f (the original function) is concave up.
a)
(-1,1) & (3,4)
b)
(-3,-2)
c)
(-2,-1)
d)
(-3,-1) & (1,3)
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