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