Applications of Differential Calculus DP Objectives: 7.4, 7.5, 7.6 Contents: Increasing and Decreasing Functions Stationary points Rates of change Optimisation

Review of Intervals

Increasing and Decreasing Functions

Sign Diagrams

1. 2. 4. 3.

Example Find the roots of the given function Label the roots on the sign diagram Check the sign of the derivative in the given interval Decide if the function is increasing or decreasing based on the sign in the sign diagram

Quick Review

Stationary Points

Example

Example:

Practice Problem

Recall the Vocabulary Increasing function Decreasing function Intervals Sign diagram Critical values Stationary Points Maximum Minimum Points of inflection

Rates of Change

Example 1

Now Try this -