Average rate of change is a mathematical concept that measures the average amount by which a quantity changes over a given interval of time or space. It is calculated by finding the slope of a line connecting two points on a graph.
The average rate of change is calculated over a specific interval, while the instantaneous rate of change is calculated at a specific point. In other words, the average rate of change gives an overall rate of change over a period of time, while the instantaneous rate of change gives the rate of change at a specific moment.
Average rate of change is used in various fields such as physics, economics, and engineering to measure and analyze changes in quantities over time. For example, it can be used to calculate average speed in a car race or to track changes in stock prices over a period of time.
To solve an average rate of change problem, you need to first identify the two points on the graph and their corresponding coordinates. Then, you can use the formula "change in y/change in x" to calculate the slope of the line connecting the two points, which represents the average rate of change.
Differentiation is the process of finding the instantaneous rate of change at a specific point. It is closely related to average rate of change because it involves finding the slope of a line tangent to a curve at a specific point, which is equivalent to finding the instantaneous rate of change at that point.