1 / 8

Curve Sketching

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?

elden
Télécharger la présentation

Curve Sketching

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Curve Sketching Lesson 5.4

  2. 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

  3. Tools for Curve Sketching • Test for concavity • Test for increasing/decreasing functions • Critical points • Zeros • Maximums and Minimums

  4. 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

  5. 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)

  6. Try It Out • Find as much as you can about the function without graphing it on the calculator

  7. 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)

  8. Assignment • Lesson 5.4 • Page 354 • Exercises 1 – 39 odd

More Related