/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 104 What is the average rate of chan... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 104

What is the average rate of change of a function?

Short Answer

Expert verified
The average rate of change of a function, from a point \((x_1, f(x_1))\) to a point \((x_2, f(x_2))\), is given by \(\frac{f(x_2)-f(x_1)}{x_2-x_1}\). This measures how much the function is changing per unit increase in the input.

Step by step solution

01

Understanding the Concept

The average rate of change of a function between two points is the change in the y-value divided by the change in the x-value. It measures how much the function is changing per unit increase in the input.
02

The Mathematical Representation

Mathematically, the average rate of change of a function \(f(x)\) from a point \((x_1, f(x_1))\) to a point \((x_2, f(x_2))\) is given by \(\frac{f(x_2)-f(x_1)}{x_2-x_1}\). This formula is similar to the one used to find the slope of a line.
03

Interpretation of the Average rate of change

A positive average rate of change indicates an increasing function, a negative one indicates a decreasing function, and zero indicates the function is constant between the two points.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

If \(f(x)=a x^{2}+b x+c\) and \(r_{1}=\frac{-b+\sqrt{b^{2}-4 a c}}{2 a}\) find \(f\left(r_{1}\right)\) without doing any algebra and explain how you arrived at your result.

Give an example of an equation that does not define \(y\) as a function of \(x\) but that does define \(x\) as a function of \(y .\)

Begin by graphing the standard quadratic function, \(f(x)=x^{2} .\) Then use transformations of this graph to graph the given function. $$ g(x)=\frac{1}{2}(x-1)^{2} $$

Then use the TRACE feature to trace along the line and find the coordinates of two points. Use these points to compute the line's slope. Check your result by using the coefficient of \(x\) in the line's equation. $$y=-3 x+6$$

Begin by graphing the absolute value function, \(f(x)=|x| .\) Then use transformations of this graph to graph the given function. $$ h(x)=|x+3|-2 $$
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Applied Mathematics

Read Explanation

Decision Maths

Read Explanation

Probability and Statistics

Read Explanation

Logic and Functions

Read Explanation

Pure Maths

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.