# Worksheet: Concavity of a Function

Q1:

Use the given graph of to find all possible intervals on which is concave upward.

• A is concave upward on .
• B is concave upward on .
• C is concave upward on .
• D is concave upward on .
• E is concave upward on .

Q2:

Use the given graph of to find the coordinates of the points of inflection.

• A
• B
• C, ,
• D,
• E, ,

Q3:

Use the given graph of to find all possible intervals on which is concave downward.

• A is concave downward on .
• B is concave downward on .
• C is concave downward on and .
• D is concave downward on .
• E is concave downward on and .

Q4:

Use the given graph of to find the coordinates of the point of inflection.

• A,
• B
• C
• D
• E

Q5:

Use the given graph of to find all possible intervals on which is concave upward.

• A is concave upward on .
• B is concave upward on .
• C is concave upward on and .
• D is concave upward on and .
• E is concave upward on and .

Q6:

Use the given graph of to find all possible intervals on which is concave downward.

• A is concave downward on .
• B is concave downward on .
• C is concave downward on and .
• D is concave downward on .
• E is concave downward on .

Q7:

The graph of the first derivative of a continuous function is shown. On what intervals is concave upward or concave downward?

• A is concave upward on and and concave downward on and .
• B is concave upward on and and concave downward on and .
• C is concave upward on , , and and concave downward on and .
• D is concave upward on and and concave downward on and .
• E is concave upward on and and concave downward on , , and .

Q8:

The graph of the first derivative of a continuous function is shown. On what intervals is concave upward or concave downward?

• A is concave upward on , , and and concave downward on and .
• B is concave upward on and and concave downward on and .
• C is concave upward on and and concave downward on .
• D is concave upward on and and concave downward on and .
• E is concave upward on and concave downward on and .