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)