# Worksheet: Interpreting Graphs of Derivatives

In this worksheet, we will practice connecting a function to the graphs of its first and second derivatives.

Q1:

The graph of a function is shown. At which point are and both positive? • Apoint
• Bpoint
• Cpoint
• Dpoint
• Epoint

Q2:

The graph of a function is shown. At which point are and both negative? • Apoint
• Bpoint
• Cpoint
• Dpoint
• Epoint

Q3:

Given that and , which of the following must be true?

• A has a local minimum at .
• B has a horizontal tangent at .
• C has a vertical tangent at .
• D has an inflection point at .
• E has a local maximum at .

Q4:

Use the given graph of a function to find the -coordinates of the inflection points of . • A has inflection points at and .
• B has inflection points at and .
• C has inflection points at and .
• D has inflection points at , , and .
• E has inflection points at and .

Q5:

The graph of the first derivative of a continuous function is shown. State the -coordinates of the inflection points of . • A has inflection points at and .
• B has inflection points at and .
• C has inflection points at , , , and .
• D has inflection points at , , and .
• E has inflection points at , , , and .

Q6:

The graph of the first derivative of a function is shown. What are the -coordinates of the inflection points of ? • A has inflection points at , , , , and .
• B has inflection points at , , and .
• C has inflection points at , , , and .
• D has inflection points at and .
• E has inflection points at and .

Q7:

Using the given graph of the function , at what values of does have inflection points? • A has inflection points when and .
• B has inflection points when and .
• C has inflection points when and .
• D has inflection points when , and.
• E has inflection points when and .

Q8:

The graph of the first derivative of a continuous function is shown. State the -coordinates of the inflection points of . • A has inflection points at and .
• B has inflection points at and .
• C has an inflection point at .
• D has inflection points at , , and .
• E has an inflection point at .

Q9:

The graph of the derivative of a function is shown. At what values of does have a local maximum or minimum? • A has a local minimum at .
• B has a local maximum at and a local minimum at .
• C has a local maximum at and a local minimum at .
• D has a local maximum at and a local minimum at .
• E has a local maximum at .

Q10:

The graph of the derivative of a function is shown. On what intervals is increasing or decreasing? • A is increasing on the interval and decreasing on the interval .
• B is increasing on the intervals and and decreasing on the interval .
• C is increasing on the interval and decreasing on the intervals and .
• D is decreasing on the interval .
• E is increasing on the interval and decreasing on the interval .

Q11:

The graph of the derivative of a function is shown. On what intervals is increasing or decreasing? • A is increasing on the intervals , , and and decreasing on the intervals and .
• B is increasing on the intervals and and decreasing on the intervals and .
• C is increasing on the intervals and and decreasing on the intervals and .
• D is increasing on the intervals and and decreasing on the intervals , , and .
• E is increasing on the intervals , , and and decreasing on the intervals , , and .

Q12:

The graph of a function is shown. At which point is negative but positive? • Apoint
• Bpoint
• Cpoint
• Dpoint
• Epoint

Q13:

The graph of the first derivative of a 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 .

Q14:

The graph of the function is shown. Determine over which intervals the function is positive. • A and
• B, , and
• D, , and
• E and

Q15:

The graph of the function is shown. Determine over which intervals the function is concave upward. • A
• B, , and
• C, , and
• D, , and
• E, , and