/*! 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. 33 Use a sign chart for f'聽to dete... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Q. 33 (page 261)

Use a sign chart for f'to determine the intervals on which each function fis increasing or decreasing. Then verify your algebraic answers with graphs from a calculator or graphing utility.

ln(x2+1)

Short Answer

Expert verified

Ans:

After inserting the root values we can find the increasing and decreasing intervals of the given function.

Intervals of the given function are

Increasing at0,鈭�

Decreasing at-鈭�,0

Step by step solution

01

Step 1. Given information:

ln(x2+1)

02

Step 2. Finding the derivative of the function:

f(x)=lnx2+1f'(x)=2xx2+1letf'(x)=0鈭�2xx2+1=0鈬�2x=x2+10鈬�2x=0x=0

03

Step 3. Inserting the root points on the number line(Sign chart):

After inserting the root values we can find the increasing and decreasing intervals of the given function.

Intervals of the given function are

Increasing at(0,鈭�)

Decreasing at(-鈭�,0)

04

Step 4. Verifying algebraic answers with graphs :

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

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)=1x-12x-2

Use a sign chart for f'to determine the intervals on which each function fis increasing or decreasing. Then verify your algebraic answers with graphs from a calculator or graphing utility.

f(x)=1sinx

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

Restate the Mean Value Theorem so that its conclusion has to do with tangent lines.

Explain the difference between two antiderivatives of the function.
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Applied Mathematics

Read Explanation

Mechanics Maths

Read Explanation

Probability and Statistics

Read Explanation

Decision Maths

Read Explanation

Discrete 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.