Specialist Maths Calculus Week 3

Theorem P Q R T Proof

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

P Q R T

Example 1 (7A1)

Solution 1

Basic Trigonometric Derivatives

Chain Rule

Example 2 (7A1)

Solution 2

Example 3 (7A1)

Solution 3

Example 4 (7A1)

Solution 4

Example 5 (7A1)

Solution 5

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.

Example 6 (7A2)

Solution 6

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

Example 6 (7B) P Q R 2 km

Solution to Example 6 Q R 2 km P

Continued max Min must occur at end points

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