A-Math: Type of Stationary Point through First Derivative

Photo Credit: mysza831

One of the applications of Differentiation is to determine the type of stationary point. This application is common in maximum and minimum problems.

There are two ways to go about finding the type of stationary point. The more frequently used method is through Second Derivative (Watch the video here). (d^2y/dx^2)

However, I'm not going to discuss on that method. Instead I want to share with you on the less popular method which is First Derivative. The reason: I have observed that last 2 years, questions appearing in the GCE 'O' level Additional Mathematics were less commonly seen, least expected and definitely more nerve breaking for candidates who aren't prepared.

Let's take a look at how First Derivative is applied.

Look at the 2 values of r which are in the yellow box. Do you know how I arrive at these values? Is there any rule?

Pay attention to the solution, notice that I get the value of r (5.03) when first derivative (dA/dr) is equal to zero.

Next to fill up the value on the right hand side, you add a little. In this case, I choose add 0.5. You may choose to add 0.1. It's fine.

On the left hand side, we subtract away 0.5 (you may choose to subtract 0.1).

As long as the addition and subtraction involve small amount like 0.1 - 0.5, you will arrive at the correct answer.

Conclusion: To determine the nature of Stationary Point, there are two methods. Using either the first or second derivative will answer the question. Also note that the approach for using second derivative is different from that of the first derivative. I hope you enjoy this post.