Constant rate of change definition

We know that objects or particles can move on different types of trajectories. Those which are moving along a straight line have the mathematical property of moving at constant rate of change. The constant rate of change definition is very simple and logical: "An object moving uniformly with respect to time, is said is moving at a constant rate of change."

Have a look at constant rate of change example

Let's take a practical constant rate of change example to easily understand the phenomenon. In the following table, you can observe that the Distance increases proportionally with Time. That means that between any two points the rate of change is the same (constant).
constant rate of change example

Understanding the average rate of change

Mathematically speaking, the "rate of change" is the slope of the line that joins two specific points. This term is also known as the average rate of change. It is very simple to find the average rate of change using simple formulas.

Studying average rate of change formula

We know that a function represents a relationship between x and y: y = f(x) where y is a dependent quantity and x an independent one. It is very easy to find the average rate of change of a function using a specific formula for this task.

In basic terms, the average rate of change calculus could be done using the following general terms:

Average Rate of Change = (change in y value)/(change in x value). In more advanced terms, the average rate of change formula could be written as δy/δx = (f(b)-f(a))/(b-a) .

In the upper formula for rate of change, (b - a) represents the change in the input of the function, f(b)-f(a) represents the change in the function f as the input change from a to b. δy/δx is the average rate of change function.

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