/*! 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. 6 Sign analyses for second derivat... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Q. 6 (page 250)

Sign analyses for second derivatives: Repeat the instructions of the previous block of problems, except find sign intervals for the second derivative f''instead of the first derivative.

f(x)=x23x

Short Answer

Expert verified

The second derivative of the given function is the local maximum at x=-1.8,and a local minimum at x=0.

Step by step solution

01

Step 1. Given Information.

The given function isf(x)=x23x.

02

Step 2. Find the second derivative. 

To find the second derivative, first, we find the first derivative then the second.

So,

f(x)=x23xf'(x)=x23xln3+2x3xf''(x)=x2ln33xln3+(2x)3xln3+2x3xln3+23xf''(x)=x2ln33xln3+4x3xln3+23x

03

Step 3. Find sign intervals for the second derivative. 

To find the sign intervals let's find the critical points from the first derivative.

So,

f'(x)=0x23xln3+2x3x=0x3x(xln3+2)=0x=0andx=鈭�2ln3x=鈭�21.09x=鈭�1.8

Thus, the critical points arex=0andx=鈭�1.8.

Now, at x=0,f''(x)>0and atx=-1.8,f''(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

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=3x-2ex

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)=x23-x13

Restate Theorem 3.3 so that its conclusion has to do with

tangent lines.

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.

role="math" localid="1648370582124" f(x)=sinx.cosx

Find the possibility graph of its derivative f'.
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Mechanics Maths

Read Explanation

Calculus

Read Explanation

Statistics

Read Explanation

Discrete Mathematics

Read Explanation

Probability and Statistics

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.