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Applications of Derivatives Review Flashcards | StudBud

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Applications of Derivatives Review

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A quick review of calculus topics dealing with the applications of the first and second derivative.

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Questions 11

Answers

1
Find the interval over which the given function is concave up.
(-∞, 1)
(-2, 4)
(1, ∞)
(-∞, -2) U (4,∞)
2
The First Derivative Test...
Determines if critical points are local extrema on f(x)
Locates point of inflection on f(x)
Locates critical points on f(x)
Determines the increasing and decreasing behavior of f(x)
3
Based on the sign chart, which of the following statements is false?
f(x) has two points of inflection
f(x) has three points of inflection
f(x) is concave up on (-∞,-6)
f(x) is concave down on (0,5)
4
Find the interval over which the given function is decreasing.
(-∞, 1)
(-∞, -2) U (4,∞)
(1, ∞)
(-2, 4)
5
Find the inflection point for the function f(x)=x⁴-x .
No point of inflection
x = 0
x = 1
x = ∛(1/4)
6
A point of inflection can be found when...
f"(x) changes signs
f'(x) changes signs
f'(x)=0 or undefined
f"(x)=0 or undefined
7
Which of the following is NOT a step when completing an optimization problem.
Test minimum or maximum value
Draw a diagram
Develop an equation to optimize
Check for change
8
The function shown here appears to have how many points of inflection?
3
4
2
5
9
Based on the sign chart, which of the following statements is false?
f(x) has a relative maximum at x=-6
f(x) has two critical points
f(x) has three critical points
f(x) has a relative minimum at x=5
10
The Second Derivative Test...
Determines the concavity of f(x)
Locates point of inflection on f(x)
Determines if critical points are local extrema on f(x)
Locates critical points on f(x)
11
The function shown here appears to have how many critical points?
3
2
5
4