Year 12/AS Pure Chapter 12.5 (Differentiation)

In this lesson we introduce and explore the concept of increasing and decreasing functions and whether a function is increasing or decreasing on a given interval (range of x-values). We also briefly introduce the second-order derivative which will be explored deeper in the next lesson.

Hyperlinks to sections of this video:

Introduction: 00:00

Solution to Warm-Up Q1: 0:36
Solution to Warm-Up Q2: 2:49
Solution to Warm-Up Q3: 5:33
Solution to Warm-Up Q4: 6:55

Introducing increasing and decreasing functions/intervals: 11:47

Worked Example 1: Showing a function of x is increasing for all x∈ℝ: 14:41
Worked Example 2: Finding the interval for which a function is decreasing: 18:23

Introduction to the Second-Order Derivative: 23:56

Worked Examples: computing second-order derivatives: 25:34

Suggested questions: 29:34

[MrBaileyMaths]

Hyperlinks to video sections for smartphones/tablets:


Solution to Warm-Up Q1: 0:36
Solution to Warm-Up Q2: 2:49
Solution to Warm-Up Q3: 5:33
Solution to Warm-Up Q4: 6:55
Introducing increasing and decreasing functions/intervals: 11:47
Worked Example 1: Showing a function of x is increasing for all x∈ℝ: 14:41
Worked Example 2: Finding the interval for which a function is decreasing: 18:23
Introduction to the Second-Order Derivative: 23:56
Worked Examples: computing second-order derivatives: 25:34
Suggested questions from textbook: 29:34