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

f(x) has three points of inflection

With the Extreme Value theorem, what is guaranteed?

If closed interval & continuous, then absolute max and min.

The Second Derivative Test...

Determines if critical points are local extrema on f(x), Determines the concavity of f(x)

The First Derivative Test...

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

With the Mean Value Theorem what is guaranteed?

if closed & cont, then f ' (x) = ( f(b) - f(a) ) / ( b - a )

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Applications of Derivatives Review- use during 4.4 if need a rev of 4.1-4.3

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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 10

Answers

1
The function shown here appears to have how many points of inflection?
2
5
3
4
2
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 up on (-∞,-6)
f(x) is concave down on (0,5)
3
Which of the following is NOT a step when completing an optimization problem.
Develop an equation to optimize
Test minimum or maximum value
Draw a diagram
Check for change
4
With the Extreme Value theorem, what is guaranteed?
If closed interval & continuous, then absolute max and min.
relative max and min
If closed interval & continuous, then relative max and min.
absolute max and min
5
The function shown here appears to have how many critical points?
4
2
3
5
6
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)
7
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 two critical points
f(x) has a relative maximum at x=-6
8
The First Derivative Test...
Locates point of inflection on f(x)
Determines the increasing and decreasing behavior of f(x)
Determines if critical points are local extrema on f(x)
Locates critical points on f(x)
9
A point of inflection can be found when...
f"(x) changes signs
f'(x)=0 or undefined
f'(x) changes signs
f"(x)=0 or undefined
10
With the Mean Value Theorem what is guaranteed?
f ' (x ) = average value
an average value
a derivative = 0
if closed & cont, then f ' (x) = ( f(b) - f(a) ) / ( b - a )

Applications of Derivatives Review- use during 4.4 if need a rev of 4.1-4.3 Flashcards | StudBud