# Worksheet: Graphing Using Derivatives

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

Q1:

Which of the following is the graph of ?

• A • B • C • D • E 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

Q3:

Which of the following is the graph of the function ?

• A • B • C • D • E Q4:

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

• A • B • C • D • E Q5:

Which of the following is the graph of the function ?

• A • B • C • D • E Q6:

Which of the following is the graph of the function ?

• A • B • C • D • E Q7:

Which of the following is the graph of the function ?

• A • B • C • D • E Q8:

Which of the following is the graph of the function on the interval ?

• 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 Q13:

Consider a function whose first derivative is . On which interval(s) is increasing?

• A
• B and
• C
• D
• E and

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 .

• A • B • C • D • E 