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Applications of Derivatives Review
Applications of Derivatives Review
12 terms
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StudBud Administration
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A quick review of calculus topics dealing with the applications of the first and second derivative.
Flashcards
12 cards
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Questions
12
Answers
1
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
2
Given f(x) =x
2
, find the value c on the interval [1, 3] for which the MVT applies.
x = 4
x = 0
x = 1/2
x = 2
3
A point of inflection can be found when...
f"(x)=0 or undefined
f'(x)=0 or undefined
f"(x) changes signs
f'(x) changes signs
4
Find the interval over which the given function is decreasing.
(-2, 4)
(-∞, -2) U (4,∞)
(1, ∞)
(-∞, 1)
5
The First Derivative Test...
Determines the increasing and decreasing behavior of f(x)
Locates point of inflection on f(x)
Locates critical points on f(x)
Determines if critical points are local extrema on f(x)
6
The function shown here appears to have how many points of inflection?
2
3
5
4
7
Which of the following is NOT a step when completing an optimization problem.
Check for change
Develop an equation to optimize
Test minimum or maximum value
Draw a diagram
8
Based on the sign chart, which of the following statements is false?
f(x) has two points of inflection
f(x) is concave down on (0,5)
f(x) has three points of inflection
f(x) is concave up on (-∞,-6)
9
The function shown here appears to have how many critical points?
5
3
4
2
10
Find the inflection point for the function f(x)=x
4
-x .
x = 1
x = 0
No point of inflection
x = ∛(1/4)
11
The Second Derivative Test...
Determines if critical points are local extrema on f(x)
Locates point of inflection on f(x)
Determines the concavity of f(x)
Locates critical points on f(x)
12
Find the interval over which the given function is concave up.
(-∞, -2) U (4,∞)
(1, ∞)
(-2, 4)
(-∞, 1)
