Year 12/AS Pure Chapter 12.6 (Differentiation)

Here, we take a look at how we can ascertain the nature of stationary points (maxima, minima, points of inflection) using two methods. The first method is by inspecting the gradient either side of the stationary point, and the second method we examine is by using the second-order derivative.

Introduction: 00:00

Solution to Warm-Up Q1: 0:50
Solution to Warm-Up Q2: 2:10
Solution to Warm-Up Q3: 4:39
Solution to Warm-Up Q4: 6:18

Finding the nature of stationary points by inspecting the gradient either side of the point: 12:47

Worked Example: Determining nature of stationary point by inspecting gradient either side: 17:11
Desmos illustration to verify results of worked example: 28:22

Determining nature of stationary points by using the second-order derivative: 29:21

Worked Example 1: Determining nature of stationary points using second derivative: 35:21
Desmos illustration to verify results of worked example: 43:48

Worked Example 2: Determing nature of stationary points using second derivative: 44:06
Desmos illustration to verify results of worked example: 52:30

Suggested Exercises: 52:56

[MrBaileyMaths]

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Solution to Warm-Up Q1: 0:50
Solution to Warm-Up Q2: 2:10
Solution to Warm-Up Q3: 4:39
Solution to Warm-Up Q4: 6:18
Finding the nature of stationary points by inspecting the gradient either side of the point: 12:47
Worked Example: Determining nature of stationary point by inspecting gradient either side: 17:11
Desmos illustration to verify results of worked example: 28:22
Determining nature of stationary points by using the second-order derivative: 29:21
Worked Example 1: Determing nature of stationary points using second derivative: 35:21
Desmos illustration to verify results of worked example: 43:48
Worked Example 2: Determing nature of stationary points using second derivative: 44:06
Desmos illustration to verify results of worked example: 52:30
Suggested Exercises: 52:56