# Worksheet: Interpreting Graphs of Derivatives

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

**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 .

**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 .

**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
- CWe need more information about .
- 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