# Lesson Worksheet: Curve Sketching using Derivatives Mathematics

In this worksheet, we will practice using derivatives to graph different functions.

Q1:

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

Q2:

Which of the following is the graph of the function ?

• 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 is the graph of the function on the interval ?

• A • B • C • D • E Q5:

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

• A • B • C • D • E Q6:

Consider the function .

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 Q7:

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 Q8:

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 Q9:

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

• A • B • C • D • E Q10:

Which of the following is the graph of ?

• A • B • C • D • E 