Chapter 5.3, Problem 3E

BuyFind*arrow_forward*

8th Edition

James Stewart

ISBN: 9781305270343

Textbook Problem

Let
*f* is the function whose graph is shown.

(a) Evaluate *g*(0), *g*(1), *g*(2), *g*(3), and *g*(6).

(b) On what interval is *g* increasing?

(c) Where does *g* have a maximum value?

(d) Sketch a rough graph of *g*.

(a)

To determine

To determine the value of

Explanation

**Given information:**

The integral function is

**Calculation:**

Show the integral function as below.

Here, *f* from *a* to *x* and *t*.

Substitute 0 for *x* in Equation (1).

Therefore, the

Draw the graph for calculation of

Determine

Substitute 1 for *x* in Equation (1).

Refer to Figure (1).

Modify Equation (2).

Substitute 1 for *b* and 2 for *h*.

Therefore, the

Draw the graph for calculation of

Determine

Substitute 2 for *x* in Equation (1).

Refer to figure 2.

The area of shaded triangle and rectangle is the function of *t* with limits 1 to 2.

Substitute

Substitute 1 for *b* and 2 for *h*.

Therefore, the

Draw the graph for calculation of

Determine

(b)

To determine

The interval *g*.

(c)

To determine

The maximum value of *g*.

(d)

To determine

**To sketch**: The rough graph of *g*.

Sect-5.1 P-1ESect-5.1 P-2ESect-5.1 P-3ESect-5.1 P-4ESect-5.1 P-5ESect-5.1 P-6ESect-5.1 P-7ESect-5.1 P-8ESect-5.1 P-13ESect-5.1 P-14E

Sect-5.1 P-15ESect-5.1 P-16ESect-5.1 P-17ESect-5.1 P-18ESect-5.1 P-19ESect-5.1 P-20ESect-5.1 P-21ESect-5.1 P-22ESect-5.1 P-23ESect-5.1 P-24ESect-5.1 P-25ESect-5.1 P-26ESect-5.1 P-27ESect-5.1 P-28ESect-5.1 P-32ESect-5.2 P-1ESect-5.2 P-2ESect-5.2 P-3ESect-5.2 P-4ESect-5.2 P-5ESect-5.2 P-6ESect-5.2 P-7ESect-5.2 P-8ESect-5.2 P-9ESect-5.2 P-10ESect-5.2 P-11ESect-5.2 P-12ESect-5.2 P-14ESect-5.2 P-15ESect-5.2 P-16ESect-5.2 P-17ESect-5.2 P-18ESect-5.2 P-19ESect-5.2 P-20ESect-5.2 P-21ESect-5.2 P-22ESect-5.2 P-23ESect-5.2 P-24ESect-5.2 P-25ESect-5.2 P-26ESect-5.2 P-27ESect-5.2 P-28ESect-5.2 P-29ESect-5.2 P-30ESect-5.2 P-33ESect-5.2 P-34ESect-5.2 P-35ESect-5.2 P-36ESect-5.2 P-37ESect-5.2 P-38ESect-5.2 P-39ESect-5.2 P-40ESect-5.2 P-41ESect-5.2 P-42ESect-5.2 P-43ESect-5.2 P-44ESect-5.2 P-45ESect-5.2 P-46ESect-5.2 P-47ESect-5.2 P-48ESect-5.2 P-49ESect-5.2 P-50ESect-5.2 P-51ESect-5.2 P-52ESect-5.2 P-53ESect-5.2 P-54ESect-5.2 P-55ESect-5.2 P-56ESect-5.2 P-57ESect-5.2 P-58ESect-5.2 P-59ESect-5.2 P-60ESect-5.2 P-61ESect-5.2 P-62ESect-5.2 P-63ESect-5.2 P-64ESect-5.2 P-65ESect-5.2 P-66ESect-5.2 P-67ESect-5.2 P-68ESect-5.2 P-69ESect-5.2 P-70ESect-5.2 P-71ESect-5.2 P-72ESect-5.2 P-73ESect-5.2 P-74ESect-5.2 P-75ESect-5.3 P-1ESect-5.3 P-2ESect-5.3 P-3ESect-5.3 P-4ESect-5.3 P-5ESect-5.3 P-6ESect-5.3 P-7ESect-5.3 P-8ESect-5.3 P-9ESect-5.3 P-10ESect-5.3 P-11ESect-5.3 P-12ESect-5.3 P-13ESect-5.3 P-14ESect-5.3 P-15ESect-5.3 P-16ESect-5.3 P-17ESect-5.3 P-18ESect-5.3 P-19ESect-5.3 P-20ESect-5.3 P-21ESect-5.3 P-22ESect-5.3 P-23ESect-5.3 P-24ESect-5.3 P-25ESect-5.3 P-26ESect-5.3 P-27ESect-5.3 P-28ESect-5.3 P-29ESect-5.3 P-30ESect-5.3 P-31ESect-5.3 P-32ESect-5.3 P-33ESect-5.3 P-34ESect-5.3 P-35ESect-5.3 P-36ESect-5.3 P-37ESect-5.3 P-38ESect-5.3 P-39ESect-5.3 P-40ESect-5.3 P-41ESect-5.3 P-42ESect-5.3 P-43ESect-5.3 P-44ESect-5.3 P-45ESect-5.3 P-46ESect-5.3 P-47ESect-5.3 P-48ESect-5.3 P-49ESect-5.3 P-50ESect-5.3 P-51ESect-5.3 P-52ESect-5.3 P-53ESect-5.3 P-54ESect-5.3 P-55ESect-5.3 P-56ESect-5.3 P-57ESect-5.3 P-58ESect-5.3 P-59ESect-5.3 P-60ESect-5.3 P-61ESect-5.3 P-62ESect-5.3 P-63ESect-5.3 P-64ESect-5.3 P-65ESect-5.3 P-66ESect-5.3 P-67ESect-5.3 P-68ESect-5.3 P-69ESect-5.3 P-70ESect-5.3 P-73ESect-5.3 P-74ESect-5.3 P-75ESect-5.3 P-76ESect-5.3 P-77ESect-5.3 P-78ESect-5.3 P-79ESect-5.3 P-80ESect-5.3 P-81ESect-5.3 P-82ESect-5.3 P-83ESect-5.3 P-84ESect-5.3 P-85ESect-5.3 P-86ESect-5.4 P-1ESect-5.4 P-2ESect-5.4 P-3ESect-5.4 P-4ESect-5.4 P-5ESect-5.4 P-6ESect-5.4 P-7ESect-5.4 P-8ESect-5.4 P-9ESect-5.4 P-10ESect-5.4 P-11ESect-5.4 P-12ESect-5.4 P-13ESect-5.4 P-14ESect-5.4 P-15ESect-5.4 P-16ESect-5.4 P-17ESect-5.4 P-18ESect-5.4 P-19ESect-5.4 P-20ESect-5.4 P-21ESect-5.4 P-22ESect-5.4 P-23ESect-5.4 P-24ESect-5.4 P-25ESect-5.4 P-26ESect-5.4 P-27ESect-5.4 P-28ESect-5.4 P-29ESect-5.4 P-30ESect-5.4 P-31ESect-5.4 P-32ESect-5.4 P-33ESect-5.4 P-34ESect-5.4 P-35ESect-5.4 P-36ESect-5.4 P-37ESect-5.4 P-38ESect-5.4 P-39ESect-5.4 P-40ESect-5.4 P-41ESect-5.4 P-42ESect-5.4 P-43ESect-5.4 P-44ESect-5.4 P-45ESect-5.4 P-46ESect-5.4 P-47ESect-5.4 P-48ESect-5.4 P-49ESect-5.4 P-50ESect-5.4 P-51ESect-5.4 P-52ESect-5.4 P-53ESect-5.4 P-54ESect-5.4 P-55ESect-5.4 P-56ESect-5.4 P-57ESect-5.4 P-58ESect-5.4 P-59ESect-5.4 P-60ESect-5.4 P-61ESect-5.4 P-62ESect-5.4 P-63ESect-5.4 P-64ESect-5.4 P-65ESect-5.4 P-66ESect-5.4 P-67ESect-5.4 P-68ESect-5.4 P-69ESect-5.4 P-70ESect-5.4 P-71ESect-5.4 P-72ESect-5.4 P-73ESect-5.5 P-1ESect-5.5 P-2ESect-5.5 P-3ESect-5.5 P-4ESect-5.5 P-5ESect-5.5 P-6ESect-5.5 P-7ESect-5.5 P-8ESect-5.5 P-9ESect-5.5 P-10ESect-5.5 P-11ESect-5.5 P-12ESect-5.5 P-13ESect-5.5 P-14ESect-5.5 P-15ESect-5.5 P-16ESect-5.5 P-17ESect-5.5 P-18ESect-5.5 P-19ESect-5.5 P-20ESect-5.5 P-21ESect-5.5 P-22ESect-5.5 P-23ESect-5.5 P-24ESect-5.5 P-25ESect-5.5 P-26ESect-5.5 P-27ESect-5.5 P-28ESect-5.5 P-29ESect-5.5 P-30ESect-5.5 P-31ESect-5.5 P-32ESect-5.5 P-33ESect-5.5 P-34ESect-5.5 P-35ESect-5.5 P-36ESect-5.5 P-37ESect-5.5 P-38ESect-5.5 P-39ESect-5.5 P-40ESect-5.5 P-41ESect-5.5 P-42ESect-5.5 P-43ESect-5.5 P-44ESect-5.5 P-45ESect-5.5 P-46ESect-5.5 P-47ESect-5.5 P-48ESect-5.5 P-49ESect-5.5 P-50ESect-5.5 P-51ESect-5.5 P-52ESect-5.5 P-53ESect-5.5 P-54ESect-5.5 P-55ESect-5.5 P-56ESect-5.5 P-57ESect-5.5 P-58ESect-5.5 P-59ESect-5.5 P-60ESect-5.5 P-61ESect-5.5 P-62ESect-5.5 P-63ESect-5.5 P-64ESect-5.5 P-65ESect-5.5 P-66ESect-5.5 P-67ESect-5.5 P-68ESect-5.5 P-69ESect-5.5 P-70ESect-5.5 P-71ESect-5.5 P-72ESect-5.5 P-73ESect-5.5 P-74ESect-5.5 P-75ESect-5.5 P-76ESect-5.5 P-77ESect-5.5 P-78ESect-5.5 P-79ESect-5.5 P-80ESect-5.5 P-81ESect-5.5 P-82ESect-5.5 P-83ESect-5.5 P-84ESect-5.5 P-85ESect-5.5 P-86ESect-5.5 P-87ESect-5.5 P-88ESect-5.5 P-89ESect-5.5 P-90ESect-5.5 P-91ESect-5.5 P-92ESect-5.5 P-93ESect-5.5 P-94ECh-5 P-1RCCCh-5 P-2RCCCh-5 P-3RCCCh-5 P-4RCCCh-5 P-5RCCCh-5 P-6RCCCh-5 P-7RCCCh-5 P-8RCCCh-5 P-9RCCCh-5 P-1RQCh-5 P-2RQCh-5 P-3RQCh-5 P-4RQCh-5 P-5RQCh-5 P-6RQCh-5 P-7RQCh-5 P-8RQCh-5 P-9RQCh-5 P-10RQCh-5 P-11RQCh-5 P-12RQCh-5 P-13RQCh-5 P-14RQCh-5 P-15RQCh-5 P-16RQCh-5 P-17RQCh-5 P-18RQCh-5 P-1RECh-5 P-2RECh-5 P-3RECh-5 P-4RECh-5 P-5RECh-5 P-6RECh-5 P-7RECh-5 P-8RECh-5 P-9RECh-5 P-10RECh-5 P-11RECh-5 P-12RECh-5 P-13RECh-5 P-14RECh-5 P-15RECh-5 P-16RECh-5 P-17RECh-5 P-18RECh-5 P-19RECh-5 P-20RECh-5 P-21RECh-5 P-22RECh-5 P-23RECh-5 P-24RECh-5 P-25RECh-5 P-26RECh-5 P-27RECh-5 P-28RECh-5 P-29RECh-5 P-30RECh-5 P-31RECh-5 P-32RECh-5 P-33RECh-5 P-34RECh-5 P-35RECh-5 P-36RECh-5 P-37RECh-5 P-38RECh-5 P-39RECh-5 P-40RECh-5 P-41RECh-5 P-42RECh-5 P-43RECh-5 P-44RECh-5 P-45RECh-5 P-46RECh-5 P-47RECh-5 P-48RECh-5 P-49RECh-5 P-50RECh-5 P-51RECh-5 P-52RECh-5 P-53RECh-5 P-54RECh-5 P-55RECh-5 P-56RECh-5 P-57RECh-5 P-58RECh-5 P-59RECh-5 P-60RECh-5 P-61RECh-5 P-62RECh-5 P-63RECh-5 P-66RECh-5 P-69RECh-5 P-70RECh-5 P-71RECh-5 P-72RECh-5 P-1PCh-5 P-2PCh-5 P-3PCh-5 P-5PCh-5 P-6PCh-5 P-7PCh-5 P-8PCh-5 P-9PCh-5 P-10PCh-5 P-11PCh-5 P-14PCh-5 P-15PCh-5 P-18PCh-5 P-19P

Calculus: Early Transcendental Functions

Finite Mathematics and Applied Calculus (MindTap Course List)

Calculus: An Applied Approach (MindTap Course List)

Multivariable Calculus

Calculus: Early Transcendentals

Precalculus: Mathematics for Calculus (Standalone Book)

Essentials Of Statistics

Essentials of Statistics for The Behavioral Sciences (MindTap Course List)

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

Calculus (MindTap Course List)

Statistics for The Behavioral Sciences (MindTap Course List)

Understanding Basic Statistics

Single Variable Calculus

Finite Mathematics

Mathematical Applications for the Management, Life, and Social Sciences

Intermediate Algebra

Probability and Statistics for Engineering and the Sciences

Mathematical Excursions (MindTap Course List)

Single Variable Calculus: Early Transcendentals

Contemporary Mathematics for Business & Consumers

Elements Of Modern Algebra

Elementary Geometry For College Students, 7e

Elementary Technical Mathematics

Trigonometry (MindTap Course List)

Calculus: Early Transcendental Functions (MindTap Course List)

Calculus of a Single Variable

Elementary Geometry for College Students

Finite Mathematics for the Managerial, Life, and Social Sciences

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

Study Guide for Stewart's Multivariable Calculus, 8th

Multivariable Calculus

Calculus (MindTap Course List)

College Algebra (MindTap Course List)

Research Methods for the Behavioral Sciences (MindTap Course List)

Introduction To Statistics And Data Analysis

Mathematics For Machine Technology

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

STATISTICS F/BUSINESS+ECONOMICS-TEXT

Mathematics: A Practical Odyssey

Research Methods for the Behavioral Sciences (MindTap Course List)