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 2

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

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 4

5. Using First, Second Derivatives Note the four possibilities for a function to be … Increasing or decreasing Concave up or concave down 5 Positive (increasing function) Negative (decreasing function) Positive (concave up) Negative (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 6

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) 7

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