Average Rate of Change of f(x) on [a,b]
The average rate of change of a function f(x) on the interval [a, b] is a measure of how quickly the function is changing on that interval
The average rate of change of a function f(x) on the interval [a, b] is a measure of how quickly the function is changing on that interval. It represents the average slope of the function over the given interval.
To calculate the average rate of change of f(x) on [a, b], you need to find the difference in the values of the function at the endpoints of the interval and divide it by the difference in the input values.
The average rate of change (ARC) is given by the formula:
ARC = (f(b) – f(a))/(b – a)
Here, f(b) represents the value of the function f(x) at the point x = b, and f(a) represents the value of the function at the point x = a. The denominator (b – a) represents the difference in the input values, which is the length of the interval.
By calculating the average rate of change of a function, you can determine the average rate at which the output varies with respect to the input on the given interval [a, b]. This concept is particularly useful in analyzing and comparing the behavior of functions over specific intervals.
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