/*! 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} Q. 11 Use the definitions of increasin... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Q. 11 (page 260)

Use the definitions of increasing and decreasing to argue that f(x)=x4 is decreasing on (鈭�鈭�,0] and increasing on [0,鈭�). Then use derivatives to argue the same thing.

Short Answer

Expert verified

The statement has been proven.

Step by step solution

01

Step 1. Given information

We have been given a function f(x)=x4.

We have to use the definitions of increasing and decreasing to argue that this function is decreasing on (鈭�鈭�,0]and increasing on [0,鈭�).

02

Step 2. Using the definition

For a and b in the interval (-鈭�,0]

Now if a<b鈮�0

Then,

role="math" localid="1648442267515" a4>b4

Thus the function is decreasing in the interval (-鈭�,0]

Also,

For a and b in the interval role="math" localid="1648442301380" [0,鈭�)

Now if 0<a<bthen,

a4<b4

Thus the function is increasing in the interval[0,鈭�)

03

Step 3. Using the derivative

The derivative of the function is given by :

f鈥�(x)=4x3

The function f鈥�(x)=4x3is always negative for x<0

The function f鈥�(x)=4x3is always positive for x>0

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

For each set of sign charts in Exercises 53鈥�62, sketch a possible graph of f.

Find the critical points of each function f .Then use a graphing utility to determine whether f has a local minimum, a local maximum, or neither at each of these critical points.

fx=sexx

Explain the difference between two antiderivatives of the function.

Sketch careful, labeled graphs of each function f in Exercises 63鈥�82 by hand, without consulting a calculator or graphing utility. As part of your work, make sign charts for the signs, roots, and undefined points of f,f',andf'', and examine any relevant limits so that you can describe all key points and behaviors of f.

f(x)=e3x-e2x

For each set of sign charts in Exercises 53鈥�62, sketch a possible graph of f.

See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Mechanics Maths

Read Explanation

Geometry

Read Explanation

Statistics

Read Explanation

Logic and Functions

Read Explanation

Applied Mathematics

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.