/*! 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 124 Explain how to find the differen... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 124

Explain how to find the difference quotient of a function \(f\) \(\frac{f(x+h)-f(x)}{h},\) if an equation for \(f\) is given.

Short Answer

Expert verified
To find the difference quotient \(\frac{f(x+h)-f(x)}{h}\) of a function \(f\), substitute \(f(x+h)\) and \(f(x)\) with the provided function, simplify the numerator, and then cancel out any common factors in the numerator and denominator.

Step by step solution

01

Identify the Function \(f\)

Before you can calculate the difference quotient, you need to know the function \(f\). Make sure this has been given or that you can find it from the information available.
02

Substitute Function into Difference Quotient

Replace \(f(x+h)\) and \(f(x)\) in the difference quotient formula \(\frac{f(x+h)-f(x)}{h}\) with the actual function \(f\). This means that wherever in the function there鈥檚 an \(x\), swap it out for \((x+h)\) to find \(f(x+h)\), and keep \(f(x)\) as it is.
03

Simplify

Simplify the expression in the numerator, \(f(x+h)-f(x)\). This will involve expanding any brackets and combining any like terms. If the function \(f\) is a polynomial, the \(h\) in some terms should cancel out during this step.
04

Cancel out Common Factors

Cancel out any common factors in the numerator and the denominator (which in this case is \(h\)). The result will be your difference quotient of the function \(f\).

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

$$\text { Solve for } y: \quad x=y^{2}-1, y \geq 0$$

Use a graphing utility to graph each function. Use \(a[-5,5,1]\) by [-5,5,1] viewing rectangle. Then find the intervals on which the function is increasing, decreasing, or constant. $$g(x)=x^{\frac{2}{3}}$$

Given an equation in \(x\) and \(y,\) how do you determine if its graph is symmetric with respect to the \(y\) -axis?

Complete the square and write the equation in standard form. Then give the center and radius of each circle and graph the equation. $$x^{2}+y^{2}-x+2 y+1=0$$

Find and simplify the difference quotient $$\frac{f(x+h)-f(x)}{h}, h \neq 0$$for the given function. $$f(x)=7$$
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Mechanics Maths

Read Explanation

Statistics

Read Explanation

Calculus

Read Explanation

Pure Maths

Read Explanation

Geometry

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.