Year 12/AS Pure Chapter 12.7 (Differentiation)

This lesson shows some applications of differentiation and the second derivative. We explore how to find turning points of functions in context by searching for when the gradient function is zero. We also look at how the second-order derivative can be employed to find out if such points are maximums or minimums. This process has many real-world applications (finding the minimum surface area for a solid, finding the maximum profit for a financial model, etc.)

Introduction: 00:00

Solution to Warm-Up Q1: 1:05
Solution to Warm-Up Q2: 2:11
Solution to Warm-Up Q3: 3:08
Solution to Warm-Up Q4: 5:36

Last lesson recap (stationary points and second-order derivatives): 10:24
Modelling with differentiation introduction and explanation: 15:24

Worked Example 1 (finding maxima/minima in context): 16:58
Worked Example 2 (finding maxima/minima in context): 24:51

Exam-Style question: 37:31

Suggested Exercises: 52:19

[MrBaileyMaths]

Hyperlinks to video sections for smartphones and tablets:


Solution to Warm-Up Q1: 1:05
Solution to Warm-Up Q2: 2:11
Solution to Warm-Up Q3: 3:08
Solution to Warm-Up Q4: 5:36
Last lesson recap (stationary points and second-order derivatives): 10:24
Modelling with differentiation introduction and explanation: 15:24
Worked Example 1 (finding maxima/minima in context): 16:58
Worked Example 2 (finding maxima/minima in context): 24:51
Exam-Style question: 37:31
Suggested Exercises: 52:19