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Curve Sketching

- Lesson 5.4

Motivation

- Graphing calculators decrease the importance of

curve sketching - So why a lesson on curve sketching?
- A calculator graph may be misleading
- What happens outside specified window?
- Calculator plots, connects points without showing

what happens between points - False asymptotes
- Curve sketching is a good way to reinforce

concepts of lessons in this chapter

Tools for Curve Sketching

- Test for concavity
- Test for increasing/decreasing functions
- Critical points
- Zeros
- Maximums and Minimums

Strategy

- Determine domain of function
- Find y-intercepts, x-intercepts (zeros)
- Check for vertical, horizontal asymptotes
- Determine values for f '(x) 0, critical points
- Determine f ''(x)
- Gives inflection points
- Test for intervals of concave up, down
- Plot intercepts, critical points, inflection

points - Connect points with smooth curve
- Check sketch with graphing calculator

Using First, Second Derivatives

- Note the four possibilities for a function to be

- Increasing or decreasing
- Concave up or concave down

f '(x)

f ''(x)

Try It Out

- Find as much as you can about the function

without graphing it on the calculator

Graphing Without the Formula

- Consider a function of this description
- Can you graph it?
- This function is continuous for all reals
- A y-intercept at (0, 2)

Assignment

- Lesson 5.4
- Page 354
- Exercises 1 39 odd

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