Average rate of change
f(b)-f(a)/b-a
The average rate of change is the amount of change in a given quantity over a specific period of time or over a specific range of values. In mathematics, the average rate of change is the ratio of the change in the value of a function to the change in the input variable over a certain range.
For example, if we have a function f(x) and we want to find the average rate of change over an interval [a, b], then the formula is:
Average rate of change = [f(b) – f(a)] / (b – a)
This formula gives us the average rate of change of f(x) over the interval [a, b]. We can also interpret the average rate of change as the slope of the secant line connecting two points on the graph of f(x) over the interval [a, b].
The average rate of change is an important concept in calculus and is used to find the instantaneous rate of change, which is the rate of change at a specific point on the graph of a function.
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