# Worksheet: Graphing Using Derivative

In this worksheet, we will practice drawing the curve of a function by finding its critical and inflection points and finding the intervals where the function is decreasing and increasing.

**Q2: **

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 .

**Q3: **

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 .

**Q4: **

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 .

**Q5: **

Using the graph, discuss the monotony of the function.

- A is increasing on the interval and decreasing on the interval .
- B is increasing on the interval and decreasing on the interval .
- C is increasing on the interval and decreasing on the interval .
- D is increasing on .

**Q6: **

Find where (if at all) the function has its local maxima and minima.

- Alocal minimum at , no local maximum
- Blocal minimum at , local maximum at
- Clocal maximum at , no local minimum
- Dlocal maximum at , local minimum

**Q7: **

Given that the curve has an inflection point at , what are the values of constants and ?

- A ,
- B ,
- C ,
- D ,

**Q8: **

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 .

**Q9: **

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 .

**Q10: **

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 an inflection point at .
- E has inflection points at and .

**Q11: **

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 maximum at .
- B has a local maximum at and a local minimum at .
- C has a local minimum at .
- D has a local maximum at and a local minimum at .
- E has a local maximum at and a local minimum at .

**Q12: **

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 interval .
- D is increasing on the interval and decreasing on the intervals and .
- E is decreasing on the interval .

**Q13: **

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

- A is increasing on and .
- B is increasing on and .
- C is increasing on only.
- D is increasing on and .
- E is increasing on only.

**Q14: **

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 .

**Q15: **

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

- A is decreasing on .
- B is decreasing on and .
- C is decreasing on , , and .
- D is decreasing on .
- E is decreasing on and .

**Q16: **

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

- A is increasing on .
- B is increasing on and .
- C is increasing on .
- D is increasing on and .
- E is increasing on .

**Q17: **

Using the graph, determine the intervals of increase and decrease of the function.

- A is increasing on the interval and decreasing on the interval .
- B is increasing on the interval and decreasing on the interval .
- C is increasing on the interval and decreasing on the interval .
- D is increasing on the interval and decreasing on the interval .
- E is increasing on .

**Q18: **

Consider the polynomial function whose graph is given below.

Use the given points and the fact that is a critical point of the function to determine .

- A
- B
- C
- D
- E

Determine the intervals where .

- A
- B
- C
- D
- E

**Q19: **

The graph of a function is shown. At which point is negative but positive?

- Apoint
- Bpoint
- Cpoint
- Dpoint
- Epoint