The First Derivative Test...

Determines if critical points are local extrema on f(x)

The Second Derivative Test...

Determines if critical points are local extrema on f(x)

Based on the sign chart, which of the following statements is false?

f(x) has three points of inflection

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Duplicate of Applications of Derivatives Review

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A quick review of calculus topics dealing with the applications of the first and second derivative. #calculus #derivatives #applicationsofderivatives #apcalculus

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Questions 12

Answers

1
The First Derivative Test...
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)
Locates point of inflection on f(x)
2
The Second Derivative Test...
Determines if critical points are local extrema on f(x)
Determines the concavity of f(x)
Locates critical points on f(x)
Locates point of inflection on f(x)
3
Given f(x) =x² , find the value c on the interval [1, 3] for which the MVT applies.
x = 4
x = 0
x = 2
x = 1/2
4
Based on the sign chart, which of the following statements is false?
f(x) has three points of inflection
f(x) has two points of inflection
f(x) is concave down on (0,5)
f(x) is concave up on (-∞,-6)
5
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
6
Find the interval over which the given function is decreasing.
(1, ∞)
(-2, 4)
(-∞, -2) U (4,∞)
(-∞, 1)
7
The function shown here appears to have how many points of inflection?
3
2
4
5
8
Find the inflection point for the function f(x)=x⁴-x .
No point of inflection
x = 0
x = 1
x = ∛(1/4)
9
Find the interval over which the given function is concave up.
(-∞, 1)
(-2, 4)
(1, ∞)
(-∞, -2) U (4,∞)
10
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 a relative minimum at x=5
f(x) has three critical points
11
Which of the following is NOT a step when completing an optimization problem.
Draw a diagram
Develop an equation to optimize
Test minimum or maximum value
Check for change
12
The function shown here appears to have how many critical points?
2
5
3
4

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