Question

What is the average rate of change of a function?

   What is the average rate of change of a function?

Precalculus

Robert Blitzer 5th Edition

Chapter 1, Problem 38

Instant Answer

Solved by Expert John Fullerton

04/01/2020

Step 1

The average rate of change is the same as the slope of a line. It is calculated as the change in the y-values divided by the change in the x-values. This means how much the y-value changes for every change in the x-value. Show more…

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Key Concepts

Secant Line

The secant line connects two points on the graph of a function. Its slope is equal to the average rate of change over the interval, providing a linear representation of the function's behavior between those points.

Average Rate of Change

The average rate of change of a function measures how much the function's output changes on average per unit change in the input over a specific interval. It captures the overall behavior of the function between two points.

Difference Quotient

This is the formula used to calculate the average rate of change, expressed as (f(b) - f(a))/(b - a). It represents the ratio of the change in the function's value to the change in the independent variable over an interval.

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