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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
Which of the following is NOT a step when completing an optimization problem.
Test minimum or maximum value
Check for change
Draw a diagram
Develop an equation to optimize
2
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
3
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)
4
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
5
If x=c is a critical number, then f(c) is a local extrema.
True
False
6
Find the interval over which the given function is concave up.
(-∞, -2) U (4,∞)
(-∞, 1)
(-2, 4)
(1, ∞)
7
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)
8
The First Derivative Test...
Determines when f'(x)=0
Locates point of inflection on f(x)
Determines the increasing and decreasing behavior of f(x)
Locates critical points on f(x)
9
Find the inflection point for the function f(x)=x⁴-x .
No point of inflection
x = 1
x = ∛(1/4)
x = 0
10
The function shown here appears to have how many critical points?
3
2
4
5
11
Find the interval over which the given function is decreasing.
(-∞, 1)
(1, ∞)
(-2, 4)
(-∞, -2) U (4,∞)