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Curve Sketching
Lesson #5 of
Unit 4. Applications of Differentiation
(Textbook 4.5)
Guidelines for Sketching a Curve
By finding below features of a function, you can create a sketch for it. Not all functions contain all of the below features.
• Domain: Possible x-values
• Intercepts: x-intercepts and y-intercept
• Symmetry: Even function, odd function, and period function
• Asymptotes: Horizontal asymptotes and vertical asymptotes
• Intervals of Increase or Decrease: Critical points and Inc/Dec Test
• Local Max and Min: First Derivative Test and Second Derivative Test
• Concavity and Points of Inflection: Concavity Test
Text p.311
Example
Sketch the curve .
Text p.313
Practice
Sketch the curve .
Text p.313
Practice
Sketch the curve .
Text p.314
Suggested Problems
Textbook p.317
2, 9, 14, 22, 42, 45
Suggested Problems - SOLUTIONS -
Textbook p.317
2)
Suggested Problems - SOLUTIONS -
Textbook p.317
9)
Suggested Problems - SOLUTIONS -
Textbook p.317
14)
Suggested Problems - SOLUTIONS -
Textbook p.317
22)
Suggested Problems - SOLUTIONS -
Textbook p.317
42)
Suggested Problems - SOLUTIONS -
Textbook p.317
45)