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AP Calculus BC Wednesday , 16 October 2013

AP Calculus BC Wednesday , 16 October 2013. OBJECTIVE TSW determine intervals of concavity and points of inflection (POI) by using the second derivative test. ASSIGNMENT DUE TEST DAY Sec. 3.3: pp. 186-187 (1-37 odd, 55-60 all) Sec. 3.4: p. 195 (1-37 eoo )

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AP Calculus BC Wednesday , 16 October 2013

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  1. AP Calculus BCWednesday, 16 October 2013 • OBJECTIVETSW determine intervals of concavity and points of inflection (POI) by using the second derivative test. • ASSIGNMENT DUE TEST DAY • Sec. 3.3: pp. 186-187 (1-37 odd, 55-60 all) • Sec. 3.4: p. 195 (1-37 eoo) • Sec. 3.4: p. 196 (49-56 all) • I will take HW questions in the middle of class. • COMING UP • QUIZ: Sec. 3.1 – 3.3 on Friday, 18 October 2013.

  2. Sec. 3.4: Concavity and the Second Derivative Test

  3. Sec. 3.4: Concavity and the Second Derivative Test

  4. Sec. 3.4: Concavity and the Second Derivative Test

  5. Sec. 3.4: Concavity and the Second Derivative Test

  6. Sec. 3.4: Concavity and the Second Derivative Test www.mathgraphs.com • Use this link to print out selected problems from the book. • If a problem has a graph on this website, the problem’s instructions will say so.

  7. Sec. 3.4: Concavity and the Second Derivative Test

  8. Sec. 3.4: Concavity and the Second Derivative Test Ex: Determine the open intervals of concavity for Domain: R 3

  9. Sec. 3.4: Concavity and the Second Derivative Test Ex: Determine the open intervals of concavity for Domain: R + – + –1 1 –2 0 2   

  10. Sec. 3.4: Concavity and the Second Derivative Test Ex: Determine the open intervals of concavity for Domain: R except ±2

  11. Sec. 3.4: Concavity and the Second Derivative Test Ex: Determine the open intervals of concavity for Domain: R except ±2 3

  12. Sec. 3.4: Concavity and the Second Derivative Test Ex: Determine the open intervals of concavity for Domain: R except ±2 + – + –2 2 –3 0 3     Never

  13. Sec. 3.4: Concavity and the Second Derivative Test Points of Inflection (POI)

  14. Sec. 3.4: Concavity and the Second Derivative Test

  15. Sec. 3.4: Concavity and the Second Derivative Test CAUTION: This is NOT a 2-way street! This does NOT imply that if f"(c) = 0 or does not exist, then (c, f(c)) is a point of inflection!

  16. Sec. 3.4: Concavity and the Second Derivative Test Ex: Determine the points of inflection and discuss the concavity of the graph of D: R + – + 0 2 –1 1 3    Explanation required f′′(x) changes sign at x = 0 andx = 2, giving POI

  17. Sec. 3.4: Concavity and the Second Derivative Test Second Derivative Test

  18. Sec. 3.4: Concavity and the Second Derivative Test Ex: Using the Second Derivative Test, find the relative extrema of Explanation required

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