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M1210: Apps of Derivatives Flashcards | StudBud
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M1210: Apps of Derivatives
M1210: Apps of Derivatives
13 terms
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A quick review of calculus topics dealing with the applications of the first and second derivative.
Flashcards
13 cards
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Practice quiz
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Questions
13
Answers
1
A point of inflection can be found when...
f"(x)=0 or undefined
f'(x) changes signs
f'(x)=0 or undefined
f"(x) changes signs
2
The Second Derivative Test...
Locates critical points on f(x)
Locates point of inflection on f(x)
Determines the concavity of f(x)
Determines if critical points are local extrema on f(x)
3
The function shown here appears to have how many critical points?
5
2
3
4
4
Given f(x) =x
2
, find the value c on the interval [1, 3] for which the MVT applies.
x = 1/2
x = 4
x = 2
x = 0
5
What is the function to maximize in this optimization problem?
V = L x W x H
P = 140 + 2x + y
P = 2x + y
A = xy
6
Based on the sign chart, which of the following statements is false?
f(x) has a relative minimum at x=5
f(x) has three critical points
f(x) has a relative maximum at x=-6
f(x) has two critical points
7
Find the interval over which the given function is decreasing.
(1, ∞)
(-∞, 1)
(-2, 4)
(-∞, -2) U (4,∞)
8
The First Derivative Test...
Determines the increasing and decreasing behavior of f(x)
Locates critical points on f(x)
Locates point of inflection on f(x)
Determines if critical points are local extrema on f(x)
9
Based on the sign chart, which of the following statements is false?
f(x) is concave down on (0,5)
f(x) has three points of inflection
f(x) has two points of inflection
f(x) is concave up on (-∞,-6)
10
Find the interval over which the given function is concave up.
(1, ∞)
(-∞, -2) U (4,∞)
(-∞, 1)
(-2, 4)
11
Find the inflection point for the function f(x)=x
4
-x .
x = 0
No point of inflection
x = ∛(1/4)
x = 1
12
What is the domain for the width of the pen in this problem (in feet)?
[20, 70]
[0, 50]
[20, 50]
[0, 70]
13
The function shown here appears to have how many points of inflection?
5
3
4
2
