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Historical Note Maria Gaetana Agnesi n 1718-1799 - Milan, Habsburg Empire (now Italy) n Oldest of 21children (3 mothers) n Wealthy (and busy) father n.

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Presentation on theme: "Historical Note Maria Gaetana Agnesi n 1718-1799 - Milan, Habsburg Empire (now Italy) n Oldest of 21children (3 mothers) n Wealthy (and busy) father n."— Presentation transcript:

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2 Historical Note Maria Gaetana Agnesi n 1718-1799 - Milan, Habsburg Empire (now Italy) n Oldest of 21children (3 mothers) n Wealthy (and busy) father n She spoke three languages n Writer/Debater of philosophy and natural science n Studied religious books and mathematics n Admired Newton n Learned Calculus from a monk - Ramiro Rampinelli n He encouraged her to write a book on Calculus - She is famous for writing that book in 1748

3 Increasing and Decreasing Functions (page 290)

4 Closed and Open Interval Notation (page 291) n There is not universal agreement on derivative interval notation. n The theorem below shows this author’s preference. n AP Exam will accept open or closed notation.

5 First and Second Derivative Summary Concepts

6 5.2 Extrema (page 300-305) Relative (Local) Maximum or Minimum Values Absolute (Global) Maximum or Minimum Value

7 Critical Numbers (page 302)

8 Critical Numbers Summary (page 300)

9 Critical Numbers (page 302)

10 Critical Numbers and Relative Extrema (page 302) Relative Extrema occur at critical numbers. However, not every critical number has a relative extrema.

11 First Derivative Test (page 302)

12 Second Derivative Test (page 303)

13 Homework Problem #3 (page 298)

14 Homework Problem #4 (page 296)

15 Homework Problem #5 (page 298)

16 Homework Problem #6 (page 298)

17 Homework Problem #7 (page 298)

18 Example 5a,5b,5c (page 295)

19 Example 2 (page 303)

20 Example 3 (page 303)

21 Example 4 (page 304)


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