Math / Calculus

QuestionIf the figure below is the graph of the derivative $f^{\prime}$ , answer the following:
Where do the points of inflection of $f$ occur? $\square$
On which interval(s) is $f$ concave down? $\square$
Note: You can earn partial credit on this problem.

Studdy Solution

STEP 1

1. The graph provided is of the derivative $f'$ .
2. Points of inflection of $f$ occur where $f'$ changes sign.
3. $f$ is concave down where $f'$ is decreasing.

STEP 2

1. Identify points of inflection of $f$ .
2. Determine intervals where $f$ is concave down.

STEP 3

Points of inflection occur where the derivative $f'$ changes sign. Look for x-values where $f'$ crosses the x-axis.

STEP 4

Examine the graph of $f'$ to identify x-values where it crosses the x-axis. These x-values are potential points of inflection for $f$ .

STEP 5

$f$ is concave down where $f'$ is decreasing. Identify intervals on the graph where $f'$ is decreasing.

STEP 6

Examine the graph to determine the intervals where $f'$ is decreasing. These intervals indicate where $f$ is concave down.
The points of inflection of $f$ occur where $f'$ changes sign, and $f$ is concave down on intervals where $f'$ is decreasing.

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QuestionIf the figure below is the graph of the derivative $f^{\prime}$ , answer the following:
Where do the points of inflection of $f$ occur? $\square$
On which interval(s) is $f$ concave down? $\square$
Note: You can earn partial credit on this problem.

Studdy Solution

STEP 1

1. The graph provided is of the derivative $f'$ .
2. Points of inflection of $f$ occur where $f'$ changes sign.
3. $f$ is concave down where $f'$ is decreasing.

STEP 2

1. Identify points of inflection of $f$ .
2. Determine intervals where $f$ is concave down.

STEP 3

Points of inflection occur where the derivative $f'$ changes sign. Look for x-values where $f'$ crosses the x-axis.

STEP 4

Examine the graph of $f'$ to identify x-values where it crosses the x-axis. These x-values are potential points of inflection for $f$ .

STEP 5

$f$ is concave down where $f'$ is decreasing. Identify intervals on the graph where $f'$ is decreasing.

STEP 6

Examine the graph to determine the intervals where $f'$ is decreasing. These intervals indicate where $f$ is concave down.
The points of inflection of $f$ occur where $f'$ changes sign, and $f$ is concave down on intervals where $f'$ is decreasing.

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QuestionIf the figure below is the graph of the derivative f′ f^{\prime} f′, answer the following:Where do the points of inflection of f f f occur? □\square□On which interval(s) is f f f concave down? □\square□Note: You can earn partial credit on this problem.

Studdy Solution

STEP 1

1. The graph provided is of the derivative f′ f' f′.2. Points of inflection of f f f occur where f′ f' f′ changes sign.3. f f f is concave down where f′ f' f′ is decreasing.

STEP 2

1. Identify points of inflection of f f f.2. Determine intervals where f f f is concave down.

STEP 3

Points of inflection occur where the derivative f′ f' f′ changes sign. Look for x-values where f′ f' f′ crosses the x-axis.

STEP 4

Examine the graph of f′ f' f′ to identify x-values where it crosses the x-axis. These x-values are potential points of inflection for f f f.

STEP 5

f f f is concave down where f′ f' f′ is decreasing. Identify intervals on the graph where f′ f' f′ is decreasing.

STEP 6

Examine the graph to determine the intervals where f′ f' f′ is decreasing. These intervals indicate where f f f is concave down. The points of inflection of f f f occur where f′ f' f′ changes sign, and f f f is concave down on intervals where f′ f' f′ is decreasing.

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Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionIf the figure below is the graph of the derivative $f^{\prime}$ , answer the following:
Where do the points of inflection of $f$ occur? $\square$
On which interval(s) is $f$ concave down? $\square$
Note: You can earn partial credit on this problem.

1. The graph provided is of the derivative $f'$ .
2. Points of inflection of $f$ occur where $f'$ changes sign.
3. $f$ is concave down where $f'$ is decreasing.

1. Identify points of inflection of $f$ .
2. Determine intervals where $f$ is concave down.

Points of inflection occur where the derivative $f'$ changes sign. Look for x-values where $f'$ crosses the x-axis.

Examine the graph of $f'$ to identify x-values where it crosses the x-axis. These x-values are potential points of inflection for $f$ .

$f$ is concave down where $f'$ is decreasing. Identify intervals on the graph where $f'$ is decreasing.

Examine the graph to determine the intervals where $f'$ is decreasing. These intervals indicate where $f$ is concave down.
The points of inflection of $f$ occur where $f'$ changes sign, and $f$ is concave down on intervals where $f'$ is decreasing.