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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?

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curve sketching

Curve Sketching

Lesson 5.4

motivation
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
Tools for Curve Sketching
  • Test for concavity
  • Test for increasing/decreasing functions
  • Critical points
  • Zeros
  • Maximums and Minimums
strategy
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
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
Try It Out
  • Find as much as you can about the function without graphing it on the calculator
graphing without the formula
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
Assignment
  • Lesson 5.4
  • Page 354
  • Exercises 1 – 39 odd