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Math
CalculusSingle Variable Calculus: Early Transcendentals, Volume I8th Edition

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Chapter 4.6, Problem 9E
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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

Solutions

Chapter
Section
Problem 1E
Problem 2E
Problem 3E
Problem 4E
Problem 5E
Problem 6E
Problem 9E
Problem 10E
Problem 13E
Problem 14E
Problem 27E
Problem 28E
Problem 29E
Problem 30E
Problem 33E
Problem 34E
Problem 35E
Problem 38E
Problem 39E
Problem 40E
BuyFindarrow_forward

Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

Produce graphs of f that reveal all the important aspects of the curve. Estimate the intervals of increase and decrease and intervals of concavity, and use calculus to find these intervals exactly.

f ( x ) = 1 + 1 x + 8 x 2 + 1 x 3

To determine

To sketch: The graph of f that reveals all important aspects of the curve and estimate the intervals of increase, decrease, and intervals of concavity.

Explanation

Given:

The function is f(x)=1+1x+8x2+1x3

Calculation:

The function is,

f(x)=1+1x+8x2+1x3 (1)

Differentiate both sides of the Equation (1)

f'(x)=0−1x2−8×2x3−3x4=−1x2−16x3−3x4 (2)

Differentiate both sides of the Equation (2)

f"(x)=2x3+16×3x4+3×4x5=2x3+48x4+12x5 (3)

Equate Equation (1) equal to 0.

f(x)=01+1x+8x2+1x3=0 (4)

Solve Equation (4).

x=−0.126754

Equate Equation (2) equal to 0.

f(x)=0−1x2−16x3−3x4=0 (5)

Equate Equation (3) equal to 0.

f(x)=02x3+48x4+12x5=0 (6)

Draw the graph of the function f by substituting different values for x.

The sketches of the function f with the important aspects are shown in Figure 1and Figure 2.

Refer figure 1 and figure 2.

The curve f is increasing on (−15.81, −0.19)

The curve f is decreasing on (−∞, −15.81) , (−0.19, 0) and (0, ∞) .

The local minimum value occurs at x=−15.81 .

The local maximum value occurs at x=−0.19 .

Therefore, the intervals of increase is on (−15.81, −0.19)_ .

Therefore, the intervals of decrease is on (−∞, −15.81)_ , (−0.19, 0)_ and (0, ∞)_ .

Calculate the extreme values (local maxima and local minima) as shown below:

Solve Equation (5).

x=−8−61  and−8+61=−15

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Chapter 4.6,
Problem 6E
Chapter 4.6,
Problem 10E
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In problems 23-36, use the rules of exponents to simplify so that only positive exponents remain. 29.

Mathematical Applications for the Management, Life, and Social Sciences

Find the radius of convergence and interval of convergence of the series. 43. n=02n(x3)nn+3

Single Variable Calculus: Early Transcendentals

Exercises If and are two ideals of the ring , prove that is an ideal of .

Elements Of Modern Algebra

Generalize the results found in Exercise 11 and 12 by answering each of the following questions. Assume that th...

Elementary Geometry For College Students, 7e

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Elementary Technical Mathematics

Use the given information and your calculator to find to the nearest tenth fo a degree if 0360. sin=0.7455 wit...

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Contemporary Mathematics for Business & Consumers

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Calculus of a Single Variable

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Finite Mathematics for the Managerial, Life, and Social Sciences

In Exercises 33 to 36, the method to be used are SSS, SAS, ASA, and AAS. Given that AE and BD, does it follow t...

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Sketching a Vector Field In Exercises 1 and 2, find F and sketch several representative vectors in the vector...

Multivariable Calculus

A right triangle has one leg with constant length 8 cm. The length of the other leg is decreasing at 3 cm/sec. ...

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

Sometimes, Always, or Never: fxy = fyx.

Study Guide for Stewart's Multivariable Calculus, 8th

Refer to the information given in Exercise 7.39. a. Calculate the mean and variance of z = total number of vehi...

Introduction To Statistics And Data Analysis

Compute 12453 . Round the answer to 3 decimal places.

Mathematics For Machine Technology

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

Research Methods for the Behavioral Sciences (MindTap Course List)

The NCAA estimates that the yearly value of a full athletic scholarship at in-state publicuniversities is 19,00...

STATISTICS F/BUSINESS+ECONOMICS-TEXT

Write each number in scientific notation. 0.000345

College Algebra (MindTap Course List)

Describe why you might be cautious about using the Internet to find answers to medical questions.

Research Methods for the Behavioral Sciences (MindTap Course List)

In exercise 3, the following estimated regression equation based on 30 observations was presented. = 17.6 + 3....

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

Finding a Potential Function In Exercises 11-18, determine whether the vector field is conservative. If it is, ...

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