1. Specialist Maths Calculus Week 3

2. Theorem P Q R T Proof

3. Proof of Theorem: Proof: P Q R T Consider the following areas

4. P Q R T

5. Example 1 (7A1)

6. Solution 1

7. Basic Trigonometric Derivatives

8. Chain Rule

9. Example 2 (7A1)

10. Solution 2

11. Example 3 (7A1)

12. Solution 3

13. Example 4 (7A1)

14. Solution 4

15. Example 5 (7A1)

16. Solution 5

17. Parametric Equations To change from parametric form to Cartesian form either: make the parameter subject of one equation and substitute into the other, or Use some sort of trig relationship.

18. Example 6 (7A2)

19. Solution 6

20. Maximum and Minimum Problems Draw clear diagram Find a relationship between variables If relation has more than 2 variables, find another relation between 2 of the variable to eliminate one variable in original relation Differentiate equate to zero and solve Draw a sign diagram for derivative Answer question asked

21. Example 6 (7B) P Q R 2 km

22. Solution to Example 6 Q R 2 km P

23. Continued 0.412 + - max Min must occur at end points

24. This Week Text Book pages 236 to 247 Exercise 7A1 Q1– 14 Exercise 7A2 Q1 – 4 Exercise 7B Q1 - 5