1. Augustin-Louis Cauchy and Derivatives

2. Warm-Up

3. Motivation Business – gain or loss in profit
Cars – figure out speed at a certain point
Health – growth in height over a period of time

4. History Born in Paris in 1789 Received early education from his father
He initially prepared himself to be a civil engineer
He entered the Ēcole Polytechnique in 1805, where he met Lagrange and Laplace who later persuaded him to study pure science.

5. Teachings He was a professor at Ēcole Polytechnique
His main job was teaching calculus and he was not satisfied with the way the foundations of the subject then stood.
His goal was to “do calculus right”
The result was one of the most famous textbooks in the history of mathematics, The Ēcole Polytechnique Course in Analysis.

6. Works He can be ranked next to Euler in volume of output
He wrote extensively in both pure and applied math
several books
789 papers, some of which are very extensive works
Cauchy wrote such lengthy articles the Academy of Sciences quickly passed a rule limiting all papers to a maximum of four pages because the printing bill was high.

7. Contributions
Cauchy gave numerous contributions to advanced mathematics
researches in convergence and divergence of infinite series
real and complex function theory
differential equations
determinants
probability
mathematical physics

8. Contributions to Calculus
Cauchy root test and Cauchy ratio test for convergence and divergence
Cauchy product of two given series
Basic concepts of limits and continuity
Definition of derivative
He used the notion of a limit as the basis for a rigorous foundation for calculus

9. The Derivative

10. Definition of Derivative

12. Steps Replace x with x+h Simplify numerator Factor h out of numerator
Divide by h
Plug in 0 for h
Evaluate slope

13. Example 1

14. Pascal’s Triangle

15. Find a buddy!

16. Practice

17. Answers

18. Recap

19. Independent Practice
Homework:
Pg. 324 #’s 1, 3, 6, 7, 11, 13, 17