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Duplicate of Monteiro Chapter 4: Applications of Derivatives Flashcards | StudBud
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Duplicate of Monteiro Chapter 4: Applications of Derivatives
Duplicate of Monteiro Chapter 4: Applications of Derivatives
50 terms
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Calculus AB Chapter 4 Review #calculus #derivatives #applicationsofderivatives #apcalculus
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Questions
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Answers
1
non-calculator
d
a
c
b
2
The change in SA S=6x
2
of a cube when the edge lengths change from a to a+dx is
2
6
10
4
3
How many POI's does the function with the second derivative of f(x)=xsinx-2 on (-10, 10) have?
four
six
zero
two
4
Answer
b
a
c
e
5
Answer ;0
b
a
c
d
6
Use the first derivative test to find the relative extrema
max at x=0
No relative extrema
Max at x=1
min at x=1
7
Answer the following using Newton's Method
d
b
c
a
8
Use the first derivative test to find the relative extrema
min at x=0
max at x=0
min at x=1
max at x=1
9
calculator active
b
d
c
a
10
Use the following photo to choose the correct response
a
d
b
c
11
no calculator
a
c
b
d
12
Find the following using MVT
a
d
c
b
13
Find the following volume
(125/12)π cm3
125 cm3
125/12 cm3
π cm3
14
Use the first derivative test to find the following
x=0
x=-4, 3
x=3
x=-4
15
Where is f(x)=3x
4
-4x
3
-12x
2
+3 decreasing?
(-∞,-1) U (0,2)
(1, 20)
(-∞,-1)
(0,2)
16
∻
.4π m2/sec
20π m2/sec
.04π m2/sec
4π m2/sec
17
A point of inflection can be found when...
f'(x) changes signs
f'(x)=0 or undefined
f"(x)=0 or undefined
f"(x) changes signs
18
When the area of an expanding circle is increasing twice as fast as its radius, the radius is
1/4
1/π
1
π
19
Answer
A decreasing when b<h
A always increasing
A decreasing when b>h
A always decreasing
20
If f"(p) < 0, then p is a local
minmum
neither
maximum
21
For what value of x does f(x)=x
3
-9x
2
-120x+6 have a local minimum
-10
10
3
4
22
use the first derivative test to find the relative extrema
min at x=3/2
min at x=3
max at x=3
max at x=3/2
23
Use linear approximation to find a line that approximates the curve at the given point.
d
a
c
b
24
↢Answer↣
d
c
b
a
25
:)
c
a
d
b
26
Answer the following related rates problem
a
b
d
c
27
Answer the following related rates problem
-7/24 ft/min
-7/8 ft/min
7/8 ft/min
7/24 ft/min
28
Answer :)
50 km/hr
75 km/hr
100 km/hr
25 km/hr
29
Which is a way to verify a max or min
Use the second derivative test
Determine concavity
Use the first derivative test
Look at the feasible domain
30
Use linear approximation to find a line that approximates the curve at the given point.
b
d
c
a
31
Answer the following related rates problem
b
a
d
c
32
Use the first derivative test to find the relative extrema
min at x=5
only max at x=0
no max or min
max at x=0 min at x=-2, 3
33
If f(x)=x
4
+4x
3
on which interval is f decreasing?
(0,∞)
(-3, ∞)
(-∞,-3)
(-3,0)
34
Find the volume of the largest right circular cone that can be inscribed in sphere of radius 5
y=5/3
y=-15/3
y=5
y=3/5
35
Solve the following using MVT
1.999
11
0
3.4
36
Given f(x) =x
2
, find the value c on the interval [1, 3] for which the MVT applies.
x = 0
x = 1/2
x = 4
x = 2
37
determine the coordinates of the absolute extrema of f(x)=x
2
+8x+15
(0,15) absolute min
(-4,-1) absolute max
(-4,-1) absolute min
(0,15) absolute max
38
Where is f(x)=3x
4
-4x
3
-12x
2
+3 increasing
(-1,0)
(-∞,∞)
(2,∞)
(-1,0) U (2,∞)
39
Answer the following related rates problem
a
b
d
c
40
Find the inflection point for the function f(x)=x
4
-x .
x = ∛(1/4)
x = 0
x = 1
No point of inflection
41
:)
c
b
d
a
42
no calculator
a
b
c
d
43
A particle is moving with position function x(t)=2t
3
-14t
2
+22t-5, t≥0 find the velocity function
v=6t2+28t+22
v=6t2+28t-22
v=6t2-28t-22
v=6t2-28t+22
44
:)
d
a
b
c
45
Answer the following question
t3-t2+4t+6
t3-t2-4t-6
9t2-1
3t2-2t+6
46
Answer the following related rates question
5 m/s
3 m/s
10 m/s
15 m/s
47
If f"(p) > 0, then p is a local
minimum
neither
maximum
48
Which of the following points can extrema occur at?
f1(c)=0
endpoints
All of the above
f1(c)=DNE
49
Answer the following related rates problem
b
a
c
d
50
f(x)=2x
3
-3x
2
-12x has a relative minimum at x=
0
1/3
-1
2
