CLASSWORK: First & Second Derivative Test

Question 1

2

y = f(x) is graph:

C

B

A

2

y = f'(x) is graph:

A

C

B

2

y = f"(x) is graph:

B

A

C

Question 2

8

The graph below shows the function y = f(x). A point of inflection is located at (0,0).
Complete the following table by writing negative, zero or positive in each box.

Question 5

6

Find the x-coordinates of the turning points on the graph of

Question 4

Let f(x) = {x^3}-{3x^2}-{24x}+{1}

2

Determine
f'(x)

1

Determine
f"(x)

5

Determine the x-coordinate of any turning points, justifying whether they are maximum or minimum points.

0

Determine the coordinate of any inflection points. Determine where the graph is concave up and concave down.

0

CLASSWORK: First & Second Derivative Test

y = f(x) is graph:

y = f'(x) is graph:

y = f"(x) is graph:

The graph below shows the function y = f(x). A point of inflection is located at (0,0).
Complete the following table by writing negative, zero or positive in each box.

Find the x-coordinates of the turning points on the graph of

Determine
f'(x)

Determine
f"(x)

Determine the x-coordinate of any turning points, justifying whether they are maximum or minimum points.

Determine the coordinate of any inflection points. Determine where the graph is concave up and concave down.

Sketch the graph of the function based off of the information determined in the previous questions. Make sure to have a proper scale.

y = f(x) is graph:

y = f'(x) is graph:

y = f"(x) is graph:

The graph below shows the function y = f(x). A point of inflection is located at (0,0).
Complete the following table by writing negative, zero or positive in each box.

Find the x-coordinates of the turning points on the graph of

Determine
f'(x)

Determine
f"(x)

Determine the x-coordinate of any turning points, justifying whether they are maximum or minimum points.

Determine the coordinate of any inflection points. Determine where the graph is concave up and concave down.

Sketch the graph of the function based off of the information determined in the previous questions. Make sure to have a proper scale.

CLASSWORK: First & Second Derivative Test

CLASSWORK: First & Second Derivative Test

y = f(x) is graph:

y = f'(x) is graph:

y = f"(x) is graph:

The graph below shows the function y = f(x). A point of inflection is located at (0,0).Complete the following table by writing negative, zero or positive in each box.

Find the x-coordinates of the turning points on the graph of

Determinef'(x)

Determinef"(x)

Determine the x-coordinate of any turning points, justifying whether they are maximum or minimum points.

Determine the coordinate of any inflection points. Determine where the graph is concave up and concave down.

Sketch the graph of the function based off of the information determined in the previous questions. Make sure to have a proper scale.

y = f(x) is graph:

y = f'(x) is graph:

y = f"(x) is graph:

The graph below shows the function y = f(x). A point of inflection is located at (0,0).Complete the following table by writing negative, zero or positive in each box.

Find the x-coordinates of the turning points on the graph of

Determinef'(x)

Determinef"(x)

Determine the x-coordinate of any turning points, justifying whether they are maximum or minimum points.

Determine the coordinate of any inflection points. Determine where the graph is concave up and concave down.

Sketch the graph of the function based off of the information determined in the previous questions. Make sure to have a proper scale.

The graph below shows the function y = f(x). A point of inflection is located at (0,0).
Complete the following table by writing negative, zero or positive in each box.

Determine
f'(x)

Determine
f"(x)

The graph below shows the function y = f(x). A point of inflection is located at (0,0).
Complete the following table by writing negative, zero or positive in each box.

Determine
f'(x)

Determine
f"(x)