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WorksheetsRelating the Graph of f, f' and f''
Total questions: 28
Worksheet time: 1hrs 13mins
Name
Class
Date
1.
What is true about the following? (This is an f graph)
a)
A
b)
B
c)
C
d)
D
2.
What is true about the following? (This is an f graph)
a)
A
b)
B
c)
C
d)
D
3.
What is true about the following? (This is an f graph)
a)
A
b)
B
c)
C
d)
D
4.
What is true about the following? (This is an f graph)
a)
A
b)
B
c)
C
d)
D
5.
What is the derivative?
a)
A
b)
B
c)
C
d)
D
6.
At which x-value is f continuous but not differentiable?
a)
a
b)
b
c)
c
d)
d
7.
Which is true?
a)
A
b)
B
c)
C
d)
D
8.
Where is the function increasing/decreasing?
a)
A
b)
B
c)
C
d)
D
9.
f' is given, which could be f?
a)
A
b)
B
c)
C
10.
Which could be f?
a)
A
b)
B
c)
C
11.
Given a graph of f'', which could be a Point of Inflection?
a)
A
b)
B
c)
C
d)
D
12.
The function f has positive 1st derivatives and a negative 2nd derivative. Which of the following could be a table of values for f ?
a)
A
b)
B
c)
C
13.
Which is true at a?
a)
f'(a) < f''(a) < f(a)
b)
f'(a) < f(a) < f''(a)
c)
f''(a) < f'(a) < f(a)
d)
f'(a) = f''(a) < f(a)
14.
Where does f(x) have a point of inflection?
a)
x = -3
b)
x = 3,-3
c)
x= -1
d)
x = -1,3
15.
What are the intervals of the graph increasing for f(x) = 2x4- 4x2 + 1
a)
(-1,0)
b)
(0,1)
c)
(-∞,-1) and (1,∞)
d)
(-1,0) and (1,∞)
16.
a)
[-2,1]
b)
[-2,3]
c)
[3,5]
d)
[0,1.5] and [3,5]
17.
a)
A
b)
B
c)
C
d)
D
18.
If f(x) is continuous and f'(x) is zero or undefined at x=a, then a is ALWAYS called a
a)
critical point
b)
absolute max
c)
absolute min
d)
inflection point
19.
If f"(x) is positive then f'(x) is
a)
increasing
b)
decreasing
c)
concave up
d)
concave down
20.
Given this graph of f'(x), on what interval(s) is f increasing?
a)
[-1,2]
b)
[0,1] U [3,4]
c)
[-1,0] U [1,3]
d)
[2,4]
21.
A bug begins to crawl up a vertical wire at time t = 0. The velocity v of the bug at time t, 0 < t < 8, is given by the function whose graph is shown behind this text. At what value of t does the bug change direction?
a)
2
b)
4
c)
6.5
d)
7
22.
A particle's speed is decreasing if
a)
it's acceleration is positive
b)
it's velocity is positive
c)
it's velocity and acceleration have the same sign
d)
it's velocity and acceleration have different signs
23.
An objects distance from its starting point at time t is given by the equation
s(t) = t3 - 6t2 - 4.
What is the speed of the object when its acceleration is 0?
a)
2
b)
-24
c)
12
d)
44
24.
a)
A
b)
B
c)
C
d)
D
25.
Use the sign chart for f'(x) and the table of f(x). There is ...
a)
a local maximum at x = -10.
b)
an absolute minimum at x = -2
c)
a local minimum at x = 20
d)
all of the above
26.
Use the sign chart for f'(x).
There is(are) ...
There is(are) ...
a)
a local maximum at x = -2.
b)
a local maximum at x = 4.
c)
local maxima at x = -2 and x = 4.
d)
no extrema.
27.
Use the sign chart for f'(x). There is(are) ...
a)
a local maximum at x = -2.
b)
a local minimum at
x = -2 and a local maximum at x = 4.
x = -2 and a local maximum at x = 4.
c)
a local maximum at
x = -2 and a local minimum at x = 4.
x = -2 and a local minimum at x = 4.
d)
no extrema.
28.
Over what interval(s) is f(x) decreasing?
a)
(-3, 1)
b)
(-∞, -5) ∪ (0, 2)
c)
(-∞, -3) ∪ (1, ∞)
d)
(-5, 0) ∪ (2, ∞)
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