Calculus: Calculating Average Rate Of Change In Functions

Average Rate of Change

Slope of secant line between two points, use to estimate instantanous rate of change at a point.

The average rate of change is a concept in calculus that measures how quickly a function is changing over a given period. It is calculated by finding the slope of the secant line between two points on a graph of a function. Mathematically, the average rate of change of a function f(x) over the interval [a, b] is given by:

average rate of change = (f(b) – f(a)) / (b – a)

This formula finds the change in the y-values divided by the change in the x-values between two points on the function. The resulting value represents the average rate at which the function is changing over the given interval.

For example, if we have the function f(x) = 2x + 3 and we want to find the average rate of change between x = 1 and x = 5, we would calculate as follows:

average rate of change = (f(5) – f(1)) / (5 – 1)
= (13 – 5) / 4
= 2

Therefore, the average rate of change of the function f(x) between x = 1 and x = 5 is 2. This value represents the average slope of the function over this interval, indicating the rate at which the function is changing from point to point.

More Answers: