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)