The First Derivative Test...

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

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

f has three points of inflection

The Second Derivative Test...

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

If the second derivative is positive which of the following is false?

There is a relative max at that point

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Lección 9.3

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Questions 14

Answers

1
A point of inflection can be found when...
f " changes signs
f '(x) =0 or undefined
f "(x)=0 or undefined
f ' changes signs
2
The First 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 increasing and decreasing behavior of f(x)
3
Based on the sign chart, which of the following statements is false?
f has three critical points
f has a relative maximum at x=-6
f has two critical points
f has a relative minimum at x = 5
4
On what intervals is F(x)=sin(x) concave up?
(3π/2, 2π)
(0, π)
(π, 2π)
(-1,0)
5
Find the interval over which the given function is concave up.
(1, ∞)
(-∞, 1)
(-∞, -2) U (4,∞)
(-2, 4)
6
If f '' is positive, then f is
concave up
decreasing
concave down
positive
7
Based on the sign chart for f ^{' '}, which of the following statements is false?
f has two points of inflection
f has three points of inflection
f is concave down on (0,5)
f is concave up on (-∞,-6)
8
Where does the first derivative of f is positive?
(- ∞, 4) ∪ (1, 2)
(- ∞, -2) ∪ (0, 3)
(- 4, 4]∪ [0, 2]
(- ∞, - 0]∪ [0, 3]
9
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)
10
Find the interval over which the given function is decreasing.
(1, ∞)
(-∞, -2) U (4,∞)
(-∞, 1)
(-2, 4)
11
Where the first derivative of f is negative, the graph is
concave down
increasing
decreasing
concave up
12
If the following is the graph of f ', on what values is f increasing?
(-∞,∞)
the function is always decreasing
(-∞,1)
(1,∞)
13
The function has:
A local maximum at x = -2
A local maximum at x = 0
A local minimun at x = -2
A local maximum at x = 4
14
If the second derivative is positive which of the following is false?
There is a relative min at that point
There is a relative max at that point
f is concave up
f ' is increasing

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