# What is a critical point in a system of equations?

I have an assignment question based around a system of nonlinear differential equations,

$$x' = f(x, y) \\ y ' = g(x, y)$$

The first part of the question is to locate and classify all the critical points (type and stability), which I have done.

The second part of the question then says that the system corresponds to a physical situation, involving a pendulum of a particular length. It defines the variables as meaning:

$x = \theta$ is the angle the [pendulum] wire makes with the verticle, and $y = \frac{-\theta'}{4}$ where $\theta'$ is the angular velocity at the end of the pendulum.

It asks me to explain the results of the first part in terms of that physical situation - specifically, "[my] answer should explain in terms of the pendulum, what the critical points are (without using the phrase 'critical points'), and something about their stability".

I am confident of being able to explain the stability based on the learning materials, but I'm not sure what a critical point exactly is in these terms - especially since I found some of them to be unstable. All of the information I can find, both in the learning materials and by googling, focuses on finding the critical points, which I have already done.

How can I understand what a critical point represents, and how that differs from some other point?