## average rate of change formula

### The average rate of change formula is used to calculate the average rate at which a quantity changes over a given interval

The average rate of change formula is used to calculate the average rate at which a quantity changes over a given interval. It is often used in calculus to measure the average rate at which a function changes over a specific domain.

The formula for average rate of change is:

Average Rate of Change = (f(b) – f(a)) / (b – a)

Here, f(b) represents the value of the function at the end of the interval, f(a) represents the value of the function at the beginning of the interval, b represents the endpoint of the interval, and a represents the starting point of the interval.

To find the average rate of change of a function, you need to substitute the given values into the formula and perform the calculations. The resulting value will give you the average rate at which the function changes per unit of the interval.

For example, let’s say we have a function f(x) = 2x + 3 and we want to find the average rate of change over the interval [1, 5]. Using the formula, we can calculate it as follows:

Average Rate of Change = (f(5) – f(1)) / (5 – 1)

= (2(5) + 3) – (2(1) + 3) / 4

= (10 + 3) – (2 + 3) / 4

= 13 – 5 / 4

= 8 / 4

= 2

Therefore, the average rate of change of the function f(x) = 2x + 3 over the interval [1, 5] is 2.

This value indicates that on average, the function increases by 2 units for every 1 unit increase in x over the interval.

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