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 .
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- D
- E
Determine the intervals where .
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Q2:
Which of the following is the graph of the function ?
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Q5:
Which of the following could be the graph of the function ? Use derivatives to sketch the function.
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Q6:
Consider the function .
Find .
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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 .
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- C0
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Which of the following could be the graph of ?
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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 ?
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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 .
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- D
Q9:
Which of the following could be the graph of the function ?
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- B
- C
- D
- E
Q10:
Which of the following is the graph of ?
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- E