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CalculusCalculus: An Applied Approach (MindTap Course List)10th Edition

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Chapter 4, Problem 46RE
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Calculus: An Applied Approach (Min...

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Ron Larson
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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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Analyzing a Graph In Exercises 45–48, analyze and sketch the graph of the function. Label any relative extrema, points of inflection, and asymptotes.

f ( x ) = e x x 2

To determine

To graph: The sketch of the function f(x)=exx2 and label the relative extrema, points of inflection and asymptotes.

Explanation

Given Information:

The provided function is f(x)=exx2.

Graph:

Consider the function, f(x)=exx2

Evaluate the first derivative of the function, by applying product rule and constant multiple rule.

f′(x)=ddx(exx2)=x2ddxe−xexddxx2(x2)2=x2e−x2xexx4=xe(x−2)xx4

Further solve as,

f′(x)=e(x−2)xx3

Set the derivative equal to zero to compute the value of x.

e(x−2)xx3=0e(x−2)x=0 x−2=0x=2 

Now, evaluate the second derivative of the function by applying product rule.

f″(x)=ddx[e(x−2)xx3]=x3ddxe(x−2)x−e(x−2)xddx(x3)(x3)2=x3[(x−2)ddx(ex)+exddx(x−2)]−e(x−2)x(3x2)x6=x3[(x−2)(ex)+ex]−e(3x3−6x2)xx6

Further solve as,

f″(x)=x3(x−2)(ex)+x3ex−e(3x3−6x2)xx6=x4e−x2x3e−xx3ex−3x3e+x6x2exx6=x4e−x4x3e+x6x2exx6=x2e(x2−4x+6)xx6

Further solve as,

f″(x)=e(x2−4x+6)xx4

Set the second derivative equal to zero, to determine the value of x

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Sect-4.1 P-1CPSect-4.1 P-2CPSect-4.1 P-3CPSect-4.1 P-4CPSect-4.1 P-5CPSect-4.1 P-1SWUSect-4.1 P-2SWUSect-4.1 P-3SWUSect-4.1 P-4SWUSect-4.1 P-5SWU
Sect-4.1 P-6SWUSect-4.1 P-7SWUSect-4.1 P-8SWUSect-4.1 P-9SWUSect-4.1 P-10SWUSect-4.1 P-11SWUSect-4.1 P-12SWUSect-4.1 P-13SWUSect-4.1 P-14SWUSect-4.1 P-15SWUSect-4.1 P-16SWUSect-4.1 P-17SWUSect-4.1 P-18SWUSect-4.1 P-1ESect-4.1 P-2ESect-4.1 P-3ESect-4.1 P-4ESect-4.1 P-5ESect-4.1 P-6ESect-4.1 P-7ESect-4.1 P-8ESect-4.1 P-9ESect-4.1 P-10ESect-4.1 P-11ESect-4.1 P-12ESect-4.1 P-13ESect-4.1 P-14ESect-4.1 P-15ESect-4.1 P-16ESect-4.1 P-17ESect-4.1 P-18ESect-4.1 P-19ESect-4.1 P-20ESect-4.1 P-21ESect-4.1 P-22ESect-4.1 P-23ESect-4.1 P-24ESect-4.1 P-25ESect-4.1 P-26ESect-4.1 P-27ESect-4.2 P-1CPSect-4.2 P-2CPSect-4.2 P-3CPSect-4.2 P-4CPSect-4.2 P-5CPSect-4.2 P-1SWUSect-4.2 P-2SWUSect-4.2 P-3SWUSect-4.2 P-4SWUSect-4.2 P-5SWUSect-4.2 P-6SWUSect-4.2 P-7SWUSect-4.2 P-8SWUSect-4.2 P-9SWUSect-4.2 P-10SWUSect-4.2 P-11SWUSect-4.2 P-12SWUSect-4.2 P-1ESect-4.2 P-2ESect-4.2 P-3ESect-4.2 P-4ESect-4.2 P-5ESect-4.2 P-6ESect-4.2 P-7ESect-4.2 P-8ESect-4.2 P-9ESect-4.2 P-10ESect-4.2 P-11ESect-4.2 P-12ESect-4.2 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P-63ESect-4.4 P-64ESect-4.4 P-65ESect-4.4 P-66ESect-4.4 P-67ESect-4.4 P-68ESect-4.4 P-69ESect-4.4 P-70ESect-4.4 P-71ESect-4.4 P-72ESect-4.4 P-73ESect-4.4 P-74ESect-4.4 P-75ESect-4.4 P-76ESect-4.4 P-77ESect-4.4 P-78ESect-4.4 P-79ESect-4.4 P-80ESect-4.4 P-81ESect-4.4 P-82ESect-4.4 P-83ESect-4.4 P-84ESect-4.4 P-85ESect-4.4 P-86ESect-4.4 P-87ESect-4.4 P-88ESect-4.4 P-89ESect-4.4 P-90ESect-4.4 P-91ESect-4.4 P-92ESect-4.4 P-93ESect-4.4 P-94ESect-4.4 P-95ESect-4.4 P-96ESect-4.4 P-97ESect-4.4 P-98ESect-4.5 P-1CPSect-4.5 P-2CPSect-4.5 P-3CPSect-4.5 P-4CPSect-4.5 P-5CPSect-4.5 P-6CPSect-4.5 P-7CPSect-4.5 P-8CPSect-4.5 P-9CPSect-4.5 P-10CPSect-4.5 P-1SWUSect-4.5 P-2SWUSect-4.5 P-3SWUSect-4.5 P-4SWUSect-4.5 P-5SWUSect-4.5 P-6SWUSect-4.5 P-7SWUSect-4.5 P-8SWUSect-4.5 P-9SWUSect-4.5 P-10SWUSect-4.5 P-1ESect-4.5 P-2ESect-4.5 P-3ESect-4.5 P-4ESect-4.5 P-5ESect-4.5 P-6ESect-4.5 P-7ESect-4.5 P-8ESect-4.5 P-9ESect-4.5 P-10ESect-4.5 P-11ESect-4.5 P-12ESect-4.5 P-13ESect-4.5 P-14ESect-4.5 P-15ESect-4.5 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P-4CPSect-4.6 P-1SWUSect-4.6 P-2SWUSect-4.6 P-3SWUSect-4.6 P-4SWUSect-4.6 P-5SWUSect-4.6 P-6SWUSect-4.6 P-7SWUSect-4.6 P-8SWUSect-4.6 P-9SWUSect-4.6 P-10SWUSect-4.6 P-11SWUSect-4.6 P-12SWUSect-4.6 P-1ESect-4.6 P-2ESect-4.6 P-3ESect-4.6 P-4ESect-4.6 P-5ESect-4.6 P-6ESect-4.6 P-7ESect-4.6 P-8ESect-4.6 P-9ESect-4.6 P-10ESect-4.6 P-11ESect-4.6 P-12ESect-4.6 P-13ESect-4.6 P-14ESect-4.6 P-15ESect-4.6 P-16ESect-4.6 P-17ESect-4.6 P-18ESect-4.6 P-19ESect-4.6 P-20ESect-4.6 P-21ESect-4.6 P-22ESect-4.6 P-23ESect-4.6 P-24ESect-4.6 P-25ESect-4.6 P-26ESect-4.6 P-27ESect-4.6 P-28ESect-4.6 P-29ESect-4.6 P-30ESect-4.6 P-31ESect-4.6 P-32ESect-4.6 P-33ESect-4.6 P-34ESect-4.6 P-35ESect-4.6 P-36ESect-4.6 P-37ESect-4.6 P-38ESect-4.6 P-39ESect-4.6 P-40ESect-4.6 P-41ESect-4.6 P-42ESect-4.6 P-43ESect-4.6 P-44ESect-4.6 P-45ESect-4.6 P-46ECh-4 P-1RECh-4 P-2RECh-4 P-3RECh-4 P-4RECh-4 P-5RECh-4 P-6RECh-4 P-7RECh-4 P-8RECh-4 P-9RECh-4 P-10RECh-4 P-11RECh-4 P-12RECh-4 P-13RECh-4 P-14RECh-4 P-15RECh-4 P-16RECh-4 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Convert the following decimals or whole numbers to percents. a. .8 b. 1.4 c. .0023 d. e. 19 f.

Contemporary Mathematics for Business & Consumers

The shrinkage of beef in the cooking process is 17%. If the chef starts with 70 lb of beef, how many pounds rem...

Elementary Technical Mathematics

Given: ABC with mB=mC=x2 Find: mBAC=x x, mBAC, and mB

Elementary Geometry For College Students, 7e

Simplify each expression. 542

Trigonometry (MindTap Course List)

Label each of the following statements as either true or false. Any idea of a ring R is a normal subgroup of th...

Elements Of Modern Algebra

Finding an Indefinite Integral In Exercises 91-108, find the indefinite integral. ex1exdx

Calculus of a Single Variable

Height At a sand and gravel plant, sand is falling off a conveyor and onto a conical pile at a rate of 10 cubic...

Calculus: Early Transcendental Functions (MindTap Course List)

In Exercises 5 to 8, state the ratio needed, and use it to find the measure of the indicated angle to the neare...

Elementary Geometry for College Students

VOTER TURNOUT BY INCOME Voter turnout drops steadily as income level declines. The following table gives the pe...

Finite Mathematics for the Managerial, Life, and Social Sciences

The polar equation of the conic with eccentricity 3 and directrix x = −7 is:

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

True or False: The Alternating Series Test may be applied to determine the convergence of

Study Guide for Stewart's Multivariable Calculus, 8th

Using First Partial Derivatives In Exercises 107 and 108, determine whether there exists a function f ( x, y ) ...

Multivariable Calculus

Slope Field In Exercises 41 and 42, use a computer algebra system to graph the slope field for the differential...

Calculus (MindTap Course List)

Winding a Chain A chain 10 feet long weighs 4 pounds per foot and is hung from a platform 20 feet above the gro...

Calculus

Express each number in scientific notation. 0.000000089

College Algebra (MindTap Course List)

Refer to the Costello Music Company time series in exercise 49. a. Deseasonalize the data and use the deseasona...

STATISTICS F/BUSINESS+ECONOMICS-TEXT

The manager of the Danvers-Hilton Resort Hotel stated that the mean guest bill for aweekend is 600 or less. A m...

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

In this chapter we identified four scales of measurement: nominal, ordinal, interval, and ratio. a. What additi...

Research Methods for the Behavioral Sciences (MindTap Course List)

A machine is 85% efficient and loses 1.3 horsepower through its drivetrain. Determine the horsepower input of t...

Mathematics For Machine Technology

Explain the distinction between science and pseudoscience.

Research Methods for the Behavioral Sciences (MindTap Course List)

Using the probabilities calculated in the previous exercise, determine if the probabilities P(hybrid|male) and ...

Introduction To Statistics And Data Analysis

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