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CalculusCalculus (MindTap Course List)8th Edition

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Chapter 3.3, Problem 12E
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Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621

Solutions

Chapter
Section
Problem 1E
Problem 2E
Problem 3E
Problem 4E
Problem 5E
Problem 6E
Problem 7E
Problem 8E
Problem 9E
Problem 10E
Problem 11E
Problem 12E
Problem 13E
Problem 14E
Problem 15E
Problem 16E
Problem 17E
Problem 18E
Problem 19E
Problem 20E
Problem 21E
Problem 22E
Problem 23E
Problem 24E
Problem 25E
Problem 26E
Problem 27E
Problem 28E
Problem 29E
Problem 30E
Problem 31E
Problem 32E
Problem 33E
Problem 34E
Problem 35E
Problem 36E
Problem 37E
Problem 38E
Problem 39E
Problem 40E
Problem 41E
Problem 42E
Problem 43E
Problem 44E
Problem 45E
Problem 46E
Problem 47E
Problem 48E
Problem 49E
Problem 50E
Problem 51E
Problem 52E
Problem 53E
Problem 54E
Problem 55E
Problem 56E
Problem 57E
Problem 58E
Problem 59E
Problem 60E
Problem 61E
Problem 62E
Problem 63E
Problem 64E
Problem 65E
Problem 66E
Problem 67E
Problem 68E
Problem 69E
Problem 70E
Problem 71E
Problem 72E
Problem 73E
Problem 74E
Problem 75E
Problem 76E
Problem 77E
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Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621
Textbook Problem

9-14

(a) Find the intervals on which f is increasing or decreasing.

(b) Find the local maximum and minimum values of f.

(c) Find the intervals of concavity and the inflection points.

f ( x ) = x x 2 + 1

To determine

(a)

To find:

The intervals on which f  is increasing or decreasing

Explanation

1) Concept:

The derivative of a function can be used to determine whether the function is increasing or decreasing on any intervals in its domain.

If f'x>0  over an interval I,  then fx is increasing on I.

If f'x<0  over an interval I, then fx is decreasing on I.

2) Calculation:

fx=xx2+1

f'x=x2+1 1-x(2x)(x2+1)2=1-x2(x2+1)2

f'x= 1-x2(x2+1)2 = (1+x)(1-x)(x2+1)2

Set f'x=0

x+1x-1

To determine

(b)

To find:

Local maximum and local minimum value of f(x)

To determine

(c)

To find:

Intervals of concavity and inflection points

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Chapter 3.3,
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Describing a SurfaceIn Exercises 36, describe the level surface F(x,y,z)=0. F(x,y,z)=36x2y2z2

Multivariable Calculus

Investigation Sketch the graphs of x2=4py for p=14,12,1,32, and 2 on the same coordinate axes. Discuss the chan...

Calculus (MindTap Course List)

HOW DO YOU SEE IT? Which point has greater differential, (2, 2) or (12,12)? Explain. (Assume that dx and d y ar...

Calculus

Express the following binary numbers as decimal numbers. 10011.01012

Mathematics For Machine Technology

Find the first four terms of the sequence. a1=-2, and an+1=2an2

College Algebra (MindTap Course List)

A large city hospital conducted a study to investigate the relationship between the number of unauthorized days...

STATISTICS F/BUSINESS+ECONOMICS-TEXT

Let z denote a random variable that has a standard normal distribution. Determine each of the following probabi...

Introduction To Statistics And Data Analysis

Consider a finite population with five elements labeled A, B, C, D, and E. Ten possible simple random samples o...

Statistics for Business & Economics, Revised (MindTap Course List)

Describe the general characteristics of the observational research design; explain its strengths and weaknesses...

Research Methods for the Behavioral Sciences (MindTap Course List)

Explain the difference among the terms research strategy, research design, and research procedure.

Research Methods for the Behavioral Sciences (MindTap Course List)

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