/*! 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 85 Find and simplify the difference... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 85

Find and simplify the difference quotient $$\frac{f(x+h)-f(x)}{h}, h \neq 0$$for the given function. $$f(x)=-2 x^{2}-x+3$$

Short Answer

Expert verified
The simplified difference quotient is \(-4x - 2h -1 .\)

Step by step solution

01

Finding f(x+h)

First, replace every \(x\) in the function \(f(x)\) with \(x+h\), to get \(f(x+h) = -2(x+h)^{2} - (x+h) +3.\)
02

Expanding f(x+h)

Next, expand the equation to get \(f(x+h) = -2(x^{2} + 2xh + h^{2}) - x - h +3. Simplify the equation further to get \(f(x+h) = -2x^{2} -4hx -2h^{2} -x -h+3.\)
03

Setup the difference quotient

Now, return to the difference quotient, and replace \(f(x+h)\) and \(f(x)\) with their respective values, to get \(\frac{-2x^{2} -4hx -2h^{2} -x-h+3 - (-2x^{2} -x+3)}{h}\). This simplifies to \(\frac{-4hx -2h^{2} -h}{h}\).
04

Simplify the difference quotient

Next, factor out \(h\) from the numerator to eliminate the denominator, the simplified difference quotient is \(-4x - 2h - 1 .\)

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

Complete the square and write the equation in standard form. Then give the center and radius of each circle and graph the equation. $$x^{2}+y^{2}+8 x+4 y+16=0$$

You invested \(\$ 80,000\) in two accounts paying \(5 \%\) and \(7 \%\) annual interest. If the total interest earned for the year was \(\$ 5200,\) how much was invested at each rate? (Section \(\mathrm{P.8}\) Example 5 )

The regular price of a computer is \(x\) dollars. Let \(f(x)=x-400\) and \(g(x)=0.75 x\) a. Describe what the functions \(f\) and \(g\) model in terms of the price of the computer. b. Find \((f \circ g)(x)\) and describe what this models in terms of the price of the computer. c. Repeat part (b) for \((g \circ f)(x)\) d. Which composite function models the greater discount on the computer, \(f^{\circ}\) g or \(g \circ f\) ? Explain.

Determine whether each statement makes sense or does not make sense, and explain your reasoning. My graph of \((x-2)^{2}+(y+1)^{2}=16\) is my graph of \(x^{2}+y^{2}=16\) translated two units right and one unit down.

Complete the square and write the equation in standard form. Then give the center and radius of each circle and graph the equation. $$x^{2}+y^{2}+8 x-2 y-8=0$$
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Discrete Mathematics

Read Explanation

Calculus

Read Explanation

Geometry

Read Explanation

Decision 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.