Curve Sketching

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# Curve Sketching - PowerPoint PPT Presentation

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?

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## PowerPoint Slideshow about 'Curve Sketching' - elden

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Presentation Transcript

### 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