Average rate of change on an interval
The average rate of change on an interval is a concept used in calculus to measure the average rate at which a quantity changes over a specific interval of time or distance
The average rate of change on an interval is a concept used in calculus to measure the average rate at which a quantity changes over a specific interval of time or distance. It is also known as the average rate of change of a function over an interval.
To calculate the average rate of change on an interval, you need the initial and final values of the function within that interval. Let’s say you have a function f(x), and you want to find its average rate of change over the interval from x = a to x = b.
The formula for the average rate of change on an interval is:
Average Rate of Change = (f(b) – f(a)) / (b – a)
Here, f(b) represents the value of the function at the endpoint of the interval (x = b), and f(a) represents the value of the function at the starting point of the interval (x = a). (b – a) represents the length of the interval.
By substituting the values of f(b), f(a), and (b – a) into the formula, you can calculate the average rate of change within that interval.
The average rate of change on an interval provides a measure of how the function behaves on average over that specific interval. It indicates the average slope of the function over the given interval and can explain the overall trend of the function during that interval.
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