# Worksheet: Graphing Using Derivatives

In this worksheet, we will practice using derivatives to graph a function.

**Q2: **

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

**Q4: **

Which of the following could be the graph of the function ? Use derivatives to sketch the function.

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- B
- C
- D
- E

**Q6: **

Which of the following is the graph of the function ?

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- B
- C
- D
- E

**Q7: **

Which of the following is the graph of the function ?

- A
- B
- C
- D
- E

**Q9: **

Consider the function .

Find all asymptotes of .

- A has a horizontal asymptote at and an oblique asymptote at .
- B has a horizontal asymptote at and an oblique asymptote at .
- C has a vertical asymptote at and an oblique asymptote at .
- D has a vertical asymptote at and an oblique asymptote at .
- E has a vertical asymptote at and an oblique asymptote at .

Find .

- A
- B
- C
- D
- E

Find and classify all critical points of .

- A has a local minimum at and a local maximum at .
- B has a local minimum at and a local maximum at .
- C has neither a local maximum nor 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 .

Find the intervals of increase and decrease for .

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

Find .

- A
- B
- C0
- D
- E

Which of the following could be the graph of ?

- A
- B
- C
- D
- E

**Q10: **

Consider the function .

Find .

- A
- B
- C
- D
- E

Find and classify the critical points of .

- A has a local minimum at and 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 .
- E has a local minimum at and a local maximum at .

Find the intervals of increase and decrease for .

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

Find .

- A
- B0
- C1
- D
- E

Which of the following is the graph of ?

- A
- B
- C
- D
- E

**Q11: **

Consider a function whose first derivative is defined as .

Which of the following statements is correct?

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

**Q12: **

Consider the function .

Use the second derivative of to determine the -values for which the concavity of the graph of changes. Which of the following graphs is the graph of ?

- A
- B
- C
- D

**Q14: **

Consider the function .

Find the equation of the oblique asymptote of the graph of to decide which of the following graphs is the graph of .

- A
- B
- C
- D

**Q15: **

Which of the following could be the graph of the function ?

- A
- B
- C
- D
- E

**Q16: **

Sketch the graph of .

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- B
- C
- D
- E