Calculus Explained | Average Rate of Change for Functions and Intervals

average rate of change

The average rate of change is a concept in mathematics that measures the average rate at which a quantity changes over a given interval

The average rate of change is a concept in mathematics that measures the average rate at which a quantity changes over a given interval. It is commonly used in calculus to describe the average rate of change of a function.

To calculate the average rate of change, you need to determine the difference between the values of the function at the beginning and end of the interval, and then divide this difference by the length of the interval. The formula for average rate of change can be expressed as:

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

Where 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, and (b – a) represents the length of the interval.

For example, let’s say you have a function f(x) = 2x + 3, and you want to calculate the average rate of change over the interval from x = 1 to x = 5. Plugging in the values into the formula, we have:

Average Rate of Change = (f(5) – f(1)) / (5 – 1)
= (2(5) + 3) – (2(1) + 3) / 4
= (13 – 5) / 4
= 8 / 4
= 2

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

The average rate of change provides a way to understand how the function behaves over a certain interval. It indicates how fast or slow the function is changing on average within that interval.

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