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Chapter 1: Problem 38

What is the average rate of change of a function?

Short Answer

Expert verified
The average rate of change of a function is calculated as the change in the function's output over the change in the input, usually expressed as \(\frac{f(b) - f(a)}{b-a}\)

Step by step solution

01

Understand the Concept

The average rate of change of a function is given by the ratio of the change in the output value to the change in the input value. This can be calculated using the formula: \[Average \ Rate \ of \ Change = \frac{f(b) - f(a)}{b-a}\] where \(f\) is the function, \(a\) and \(b\) are the input values.
02

Substitute the Values

Substitute the values of \(a\), \(b\), \(f(a)\), and \(f(b)\) in the above formula. It is important to note that \(a\) and \(b\) are the x-values of two points on the function, and \(f(a)\) and \(f(b)\) are the respective y-values of these two points.
03

Compute

After substituting values, execute the arithmetic operations to get the average rate of the function.

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