You are to complete this BL by 13/5 11:59pm.
In this BL session, you will be covering:
Chapter 5.2 Applications of Differentiation (5.2.2 Rates of Change to 5.2.3 Maxima and Minima Problems)
5.2.2 Rates of Change
5.2.3 Maxima and Minima Problems
As you carry out the learning activities, you should fill up your lecture notes.
You should take 1 hour to complete this lesson.
Before we begin the lesson, let us consider a classic connected rates of change question: The rate of change of the water level as the cone gets filled up!
Suppose the cone on the right is filled by water at a constant rate of 1 ml/s. How should the animation look?
Now, if we use a model of the situation, without using connected rates of change, our animation might just fill the cone where the height increases at a constant rate.
[Click the play button ▶️ to see the animation!]
However, this is rather unnatural.
We need more water to fill the cone when the water level increases. But since the cone is filled at a constant rate, we would expect the height of the water to grow at a slower pace.
Using some connected rates of change, we will be able to account for that inconsistency.
[Click the play button ▶️ to see the animation!]
Now, the animation of water filling the cone is much more natural.
Through the first half, we hope you will review your understanding of connected rates of change and develop a better appreciation of it.
Go through the lesson video for 5.2.2 Rates of Change.
Please fill your notes for pages 7 to 8.
Oh you have found me! Don't click the egg!
In the next section, we will see Maxima and Minima Problems.
In essence, we are trying to use Mathematics to optimise specific outputs given certain constraints.
Please fill your notes for pages 9 to 12.
Test yourself! Complete the following Quiz to assess your understanding and end off the BL session.