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Chapter 2: Problem 36

What is the average rate of change of a function?

Short Answer

Expert verified
The average rate of change of a function is the ratio of the change in the function value to the change in the independent variable. It is calculated as \[ \frac{f(b) - f(a)}{b - a} \] over any interval [a, b] on the function's domain.

Step by step solution

01

Understanding the Concept

The average rate of change is calculated as follows: \[ \text{Average Rate of Change} = \frac{\text{change in } y}{\text{change in } x} \] This refers to the change in the value of the function (y) over the change in the independent variable (x).
02

Choosing an Interval

The interval chosen must be clear. In most cases this will be given in the problem, for example from \(x = a\) to \(x = b\). If no specific interval is given we are referring to the average rate of change of the function over its entire domain.
03

Applying the Formula

If we have the function values at \(x = a\) and \(x = b\) as \(f(a)\) and \(f(b)\) respectively, we substitute these into our formula, the average rate of change becomes \[ \frac{f(b) - f(a)}{b - a} \].

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Most popular questions from this chapter

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