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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
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
2
The function shown here appears to have how many critical points?
4
3
5
2
3
Find the inflection point for the function f(x)=x⁴-x .
x = 0
x = 1
No point of inflection
x = ∛(1/4)
4
The First Derivative Test...
Locates point of inflection on f(x)
Determines if critical points are local extrema on f(x)
Locates critical points on f(x)
Determines the increasing and decreasing behavior of f(x)
5
Based on the sign chart, which of the following statements is false?
f(x) has three critical points
f(x) has a relative minimum at x=5
f(x) has a relative maximum at x=-6
f(x) has two critical points
6
Based on the sign chart, which of the following statements is false?
f(x) has two points of inflection
f(x) is concave up on (-∞,-6)
f(x) is concave down on (0,5)
f(x) has three points of inflection
7
Given f(x) =x² , find the value c on the interval [1, 3] for which the MVT applies.
x = 0
x = 2
x = 1/2
x = 4
8
Find the interval over which the given function is concave up.
(1, ∞)
(-∞, 1)
(-∞, -2) U (4,∞)
(-2, 4)
9
Which of the following is NOT a step when completing an optimization problem.
Test minimum or maximum value
Develop an equation to optimize
Check for change
Draw a diagram
10
The Second Derivative Test...
Locates critical points on f(x)
Locates point of inflection on f(x)
Determines if critical points are local extrema on f(x)
Determines the concavity of f(x)
11
Find the interval over which the given function is decreasing.
(-2, 4)
(-∞, 1)
(1, ∞)
(-∞, -2) U (4,∞)