# Average Rate of Change Calculator

Instructions: Use Average Rate of Change Calculator, to get a step-by-step calculation of the average rate of change of function between two points. You need to provide the points $$(t_1, y_1)$$ and $$(t_2, y_2)$$, and this calculator will estimate the average rate of change:

First t ($$t_1$$) =
First y ($$f(t_1)$$) =
Second t ($$t_2$$) =
Second y: ($$f(t_2)$$) =

## Average Rate of Change Calculator

The idea of this net change calculator is to estimate how much the given function changes per unit of time. Indeed, the average rate of change is defined as

$\text{Average Rate of Change} = \displaystyle\frac{\Delta y}{\Delta t}$

This is, it corresponds to the ratio of the net change in y ($$\Delta y$$) and the net change in t ($$\Delta t$$).

### Is the average rate of change of a function constant?

Not necessarily. The average rate of change is computed over a certain interval. If you change the interval, the average rate of change can perfectly change as well.

### Can we say that the rate of change is the same as slope?

Not always. Indeed, that only happens when the function is linear (its graph is a straight line). When the function is not linear, then the "slope" is defined locally by its derivative at each specific point. Also, we need to understand that the average rate of change ultimately is computed over an interval, so it can be changing based on the interval chosen.

The average rate of change measures the slope of the line that passes through two given points $$(t_1, y_1)$$ and $$(t_2, y_2)$$. As $$t_1$$ approaches to $$t_2$$, the average rate of change will look more and more like the slope of the tangent line.

### What is the difference with the instant rate of change?

The instant rate of change is obtained when the size of the interval for which the average rate of change is computed becomes smaller and smaller. Technically, the instant rate of change corresponds to the limit of the average rate of change, when the size of the interval approaches to zero, which is associated with the derivative of the function.