BuyFindarrow_forward

Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

Solutions

Chapter
Section
BuyFindarrow_forward

Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

Find the absolute maximum and absolute minimum values of f on the given interval.

f(t) = t + cot (t/2), [π/4, 7π/4]

To determine

To find: The absolute maximum and absolute minimum of the given function.

Explanation

Given:

The function f(t)=t+cot(t2) in the interval [π4,7π4] .

Calculation:

Obtain the first derivative of the given function.

f(t)=ddt(t+cot(t2))=ddt(t)+ddt(cot(t2))=1+(csc2(t2))ddt(t2)(ddt(cott=csc2t))=1csc2(t2)(12)

Set f(t)=0 and obtain the critical numbers.

1csc2(t2)(12)=0csc2(t2)=2csc(t2)=±2t2=π4,t2=3π4

Hence, the critical numbers are  t=π2,t=3π2

Here, both the critical numbers are lies in the given interval [π4,7π4] .

Apply the extreme values of the given interval and the critical numbers in f(t) .

Substitute t=π4 in f(t) ,

f(π4)=π4+cot(π42)=π4+cot(π8)=π4+cot(π8)3

Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started
Sect-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-4.1 P-28ESect-4.1 P-29ESect-4.1 P-30ESect-4.1 P-31ESect-4.1 P-32ESect-4.1 P-33ESect-4.1 P-34ESect-4.1 P-35ESect-4.1 P-36ESect-4.1 P-37ESect-4.1 P-38ESect-4.1 P-39ESect-4.1 P-40ESect-4.1 P-41ESect-4.1 P-42ESect-4.1 P-43ESect-4.1 P-44ESect-4.1 P-45ESect-4.1 P-46ESect-4.1 P-47ESect-4.1 P-48ESect-4.1 P-49ESect-4.1 P-50ESect-4.1 P-51ESect-4.1 P-52ESect-4.1 P-53ESect-4.1 P-54ESect-4.1 P-55ESect-4.1 P-56ESect-4.1 P-57ESect-4.1 P-58ESect-4.1 P-59ESect-4.1 P-60ESect-4.1 P-61ESect-4.1 P-62ESect-4.1 P-63ESect-4.1 P-64ESect-4.1 P-65ESect-4.1 P-66ESect-4.1 P-67ESect-4.1 P-68ESect-4.1 P-69ESect-4.1 P-70ESect-4.1 P-71ESect-4.1 P-72ESect-4.1 P-73ESect-4.1 P-74ESect-4.1 P-75ESect-4.1 P-76ESect-4.1 P-77ESect-4.1 P-78ESect-4.1 P-79ESect-4.1 P-80ESect-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 P-13ESect-4.2 P-14ESect-4.2 P-15ESect-4.2 P-16ESect-4.2 P-17ESect-4.2 P-18ESect-4.2 P-19ESect-4.2 P-20ESect-4.2 P-21ESect-4.2 P-22ESect-4.2 P-23ESect-4.2 P-24ESect-4.2 P-25ESect-4.2 P-26ESect-4.2 P-27ESect-4.2 P-28ESect-4.2 P-29ESect-4.2 P-30ESect-4.2 P-31ESect-4.2 P-32ESect-4.2 P-33ESect-4.2 P-34ESect-4.2 P-36ESect-4.2 P-37ESect-4.2 P-38ESect-4.3 P-1ESect-4.3 P-2ESect-4.3 P-3ESect-4.3 P-4ESect-4.3 P-5ESect-4.3 P-6ESect-4.3 P-7ESect-4.3 P-8ESect-4.3 P-9ESect-4.3 P-10ESect-4.3 P-11ESect-4.3 P-12ESect-4.3 P-13ESect-4.3 P-14ESect-4.3 P-15ESect-4.3 P-16ESect-4.3 P-17ESect-4.3 P-18ESect-4.3 P-19ESect-4.3 P-20ESect-4.3 P-21ESect-4.3 P-22ESect-4.3 P-23ESect-4.3 P-24ESect-4.3 P-25ESect-4.3 P-26ESect-4.3 P-27ESect-4.3 P-28ESect-4.3 P-29ESect-4.3 P-30ESect-4.3 P-31ESect-4.3 P-32ESect-4.3 P-33ESect-4.3 P-34ESect-4.3 P-35ESect-4.3 P-36ESect-4.3 P-37ESect-4.3 P-38ESect-4.3 P-39ESect-4.3 P-40ESect-4.3 P-41ESect-4.3 P-42ESect-4.3 P-43ESect-4.3 P-44ESect-4.3 P-45ESect-4.3 P-46ESect-4.3 P-47ESect-4.3 P-48ESect-4.3 P-49ESect-4.3 P-50ESect-4.3 P-51ESect-4.3 P-52ESect-4.3 P-53ESect-4.3 P-54ESect-4.3 P-55ESect-4.3 P-56ESect-4.3 P-57ESect-4.3 P-58ESect-4.3 P-59ESect-4.3 P-60ESect-4.3 P-61ESect-4.3 P-62ESect-4.3 P-66ESect-4.3 P-67ESect-4.3 P-68ESect-4.3 P-69ESect-4.3 P-70ESect-4.3 P-71ESect-4.3 P-72ESect-4.3 P-73ESect-4.3 P-74ESect-4.3 P-75ESect-4.3 P-76ESect-4.3 P-77ESect-4.3 P-78ESect-4.3 P-79ESect-4.3 P-80ESect-4.3 P-81ESect-4.3 P-82ESect-4.3 P-83ESect-4.3 P-84ESect-4.3 P-85ESect-4.3 P-86ESect-4.3 P-87ESect-4.3 P-88ESect-4.3 P-89ESect-4.3 P-90ESect-4.3 P-92ESect-4.3 P-93ESect-4.4 P-1ESect-4.4 P-2ESect-4.4 P-3ESect-4.4 P-4ESect-4.4 P-5ESect-4.4 P-6ESect-4.4 P-7ESect-4.4 P-8ESect-4.4 P-9ESect-4.4 P-10ESect-4.4 P-11ESect-4.4 P-12ESect-4.4 P-13ESect-4.4 P-14ESect-4.4 P-15ESect-4.4 P-16ESect-4.4 P-17ESect-4.4 P-18ESect-4.4 P-19ESect-4.4 P-20ESect-4.4 P-21ESect-4.4 P-22ESect-4.4 P-23ESect-4.4 P-24ESect-4.4 P-25ESect-4.4 P-26ESect-4.4 P-27ESect-4.4 P-28ESect-4.4 P-29ESect-4.4 P-30ESect-4.4 P-31ESect-4.4 P-32ESect-4.4 P-33ESect-4.4 P-34ESect-4.4 P-35ESect-4.4 P-36ESect-4.4 P-37ESect-4.4 P-38ESect-4.4 P-39ESect-4.4 P-40ESect-4.4 P-41ESect-4.4 P-42ESect-4.4 P-43ESect-4.4 P-44ESect-4.4 P-45ESect-4.4 P-46ESect-4.4 P-47ESect-4.4 P-48ESect-4.4 P-49ESect-4.4 P-50ESect-4.4 P-51ESect-4.4 P-52ESect-4.4 P-53ESect-4.4 P-54ESect-4.4 P-55ESect-4.4 P-56ESect-4.4 P-57ESect-4.4 P-58ESect-4.4 P-59ESect-4.4 P-60ESect-4.4 P-61ESect-4.4 P-62ESect-4.4 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-4.5 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 P-16ESect-4.5 P-17ESect-4.5 P-18ESect-4.5 P-19ESect-4.5 P-20ESect-4.5 P-21ESect-4.5 P-22ESect-4.5 P-23ESect-4.5 P-24ESect-4.5 P-25ESect-4.5 P-26ESect-4.5 P-27ESect-4.5 P-28ESect-4.5 P-29ESect-4.5 P-30ESect-4.5 P-31ESect-4.5 P-32ESect-4.5 P-33ESect-4.5 P-34ESect-4.5 P-35ESect-4.5 P-36ESect-4.5 P-37ESect-4.5 P-38ESect-4.5 P-39ESect-4.5 P-40ESect-4.5 P-41ESect-4.5 P-42ESect-4.5 P-43ESect-4.5 P-44ESect-4.5 P-45ESect-4.5 P-46ESect-4.5 P-47ESect-4.5 P-48ESect-4.5 P-49ESect-4.5 P-50ESect-4.5 P-51ESect-4.5 P-52ESect-4.5 P-53ESect-4.5 P-54ESect-4.5 P-55ESect-4.5 P-56ESect-4.5 P-57ESect-4.5 P-58ESect-4.5 P-59ESect-4.5 P-60ESect-4.5 P-61ESect-4.5 P-62ESect-4.5 P-63ESect-4.5 P-64ESect-4.5 P-65ESect-4.5 P-66ESect-4.5 P-67ESect-4.5 P-68ESect-4.5 P-69ESect-4.5 P-70ESect-4.5 P-71ESect-4.5 P-72ESect-4.5 P-73ESect-4.5 P-74ESect-4.5 P-75ESect-4.5 P-76ESect-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-9ESect-4.6 P-10ESect-4.6 P-13ESect-4.6 P-14ESect-4.6 P-27ESect-4.6 P-28ESect-4.6 P-29ESect-4.6 P-30ESect-4.6 P-33ESect-4.6 P-34ESect-4.6 P-35ESect-4.6 P-38ESect-4.6 P-39ESect-4.6 P-40ESect-4.7 P-1ESect-4.7 P-2ESect-4.7 P-3ESect-4.7 P-4ESect-4.7 P-5ESect-4.7 P-6ESect-4.7 P-7ESect-4.7 P-8ESect-4.7 P-9ESect-4.7 P-10ESect-4.7 P-11ESect-4.7 P-12ESect-4.7 P-13ESect-4.7 P-14ESect-4.7 P-15ESect-4.7 P-16ESect-4.7 P-17ESect-4.7 P-18ESect-4.7 P-19ESect-4.7 P-20ESect-4.7 P-21ESect-4.7 P-22ESect-4.7 P-23ESect-4.7 P-24ESect-4.7 P-25ESect-4.7 P-26ESect-4.7 P-27ESect-4.7 P-28ESect-4.7 P-29ESect-4.7 P-30ESect-4.7 P-31ESect-4.7 P-32ESect-4.7 P-33ESect-4.7 P-34ESect-4.7 P-35ESect-4.7 P-36ESect-4.7 P-37ESect-4.7 P-38ESect-4.7 P-39ESect-4.7 P-40ESect-4.7 P-41ESect-4.7 P-42ESect-4.7 P-43ESect-4.7 P-44ESect-4.7 P-45ESect-4.7 P-46ESect-4.7 P-47ESect-4.7 P-48ESect-4.7 P-49ESect-4.7 P-50ESect-4.7 P-51ESect-4.7 P-52ESect-4.7 P-53ESect-4.7 P-54ESect-4.7 P-55ESect-4.7 P-56ESect-4.7 P-57ESect-4.7 P-58ESect-4.7 P-59ESect-4.7 P-60ESect-4.7 P-61ESect-4.7 P-62ESect-4.7 P-63ESect-4.7 P-64ESect-4.7 P-65ESect-4.7 P-66ESect-4.7 P-67ESect-4.7 P-68ESect-4.7 P-69ESect-4.7 P-70ESect-4.7 P-71ESect-4.7 P-72ESect-4.7 P-73ESect-4.7 P-74ESect-4.7 P-75ESect-4.7 P-76ESect-4.7 P-77ESect-4.7 P-78ESect-4.7 P-79ESect-4.7 P-80ESect-4.7 P-81ESect-4.7 P-82ESect-4.8 P-1ESect-4.8 P-2ESect-4.8 P-3ESect-4.8 P-4ESect-4.8 P-5ESect-4.8 P-6ESect-4.8 P-7ESect-4.8 P-8ESect-4.8 P-9ESect-4.8 P-10ESect-4.8 P-11ESect-4.8 P-12ESect-4.8 P-13ESect-4.8 P-14ESect-4.8 P-15ESect-4.8 P-16ESect-4.8 P-17ESect-4.8 P-18ESect-4.8 P-19ESect-4.8 P-20ESect-4.8 P-21ESect-4.8 P-22ESect-4.8 P-23ESect-4.8 P-24ESect-4.8 P-25ESect-4.8 P-26ESect-4.8 P-27ESect-4.8 P-29ESect-4.8 P-30ESect-4.8 P-32ESect-4.8 P-33ESect-4.8 P-34ESect-4.8 P-35ESect-4.8 P-36ESect-4.8 P-37ESect-4.8 P-39ESect-4.8 P-40ESect-4.8 P-41ESect-4.8 P-42ESect-4.9 P-1ESect-4.9 P-2ESect-4.9 P-3ESect-4.9 P-4ESect-4.9 P-5ESect-4.9 P-6ESect-4.9 P-7ESect-4.9 P-8ESect-4.9 P-9ESect-4.9 P-10ESect-4.9 P-11ESect-4.9 P-12ESect-4.9 P-13ESect-4.9 P-14ESect-4.9 P-15ESect-4.9 P-16ESect-4.9 P-17ESect-4.9 P-18ESect-4.9 P-19ESect-4.9 P-20ESect-4.9 P-21ESect-4.9 P-22ESect-4.9 P-25ESect-4.9 P-26ESect-4.9 P-27ESect-4.9 P-28ESect-4.9 P-29ESect-4.9 P-30ESect-4.9 P-31ESect-4.9 P-32ESect-4.9 P-33ESect-4.9 P-34ESect-4.9 P-35ESect-4.9 P-36ESect-4.9 P-37ESect-4.9 P-38ESect-4.9 P-39ESect-4.9 P-40ESect-4.9 P-41ESect-4.9 P-42ESect-4.9 P-43ESect-4.9 P-44ESect-4.9 P-45ESect-4.9 P-46ESect-4.9 P-47ESect-4.9 P-48ESect-4.9 P-49ESect-4.9 P-50ESect-4.9 P-51ESect-4.9 P-52ESect-4.9 P-53ESect-4.9 P-54ESect-4.9 P-55ESect-4.9 P-56ESect-4.9 P-57ESect-4.9 P-58ESect-4.9 P-59ESect-4.9 P-60ESect-4.9 P-61ESect-4.9 P-62ESect-4.9 P-63ESect-4.9 P-64ESect-4.9 P-65ESect-4.9 P-66ESect-4.9 P-67ESect-4.9 P-68ESect-4.9 P-69ESect-4.9 P-70ESect-4.9 P-71ESect-4.9 P-72ESect-4.9 P-73ESect-4.9 P-74ESect-4.9 P-75ESect-4.9 P-76ESect-4.9 P-77ESect-4.9 P-79ECh-4 P-1RCCCh-4 P-2RCCCh-4 P-3RCCCh-4 P-4RCCCh-4 P-5RCCCh-4 P-6RCCCh-4 P-7RCCCh-4 P-8RCCCh-4 P-9RCCCh-4 P-10RCCCh-4 P-11RCCCh-4 P-1RQCh-4 P-2RQCh-4 P-3RQCh-4 P-4RQCh-4 P-5RQCh-4 P-6RQCh-4 P-7RQCh-4 P-8RQCh-4 P-9RQCh-4 P-10RQCh-4 P-11RQCh-4 P-12RQCh-4 P-13RQCh-4 P-14RQCh-4 P-15RQCh-4 P-16RQCh-4 P-17RQCh-4 P-18RQCh-4 P-19RQCh-4 P-20RQCh-4 P-21RQCh-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 P-17RECh-4 P-18RECh-4 P-19RECh-4 P-20RECh-4 P-21RECh-4 P-22RECh-4 P-23RECh-4 P-24RECh-4 P-25RECh-4 P-26RECh-4 P-27RECh-4 P-28RECh-4 P-29RECh-4 P-30RECh-4 P-31RECh-4 P-32RECh-4 P-33RECh-4 P-34RECh-4 P-35RECh-4 P-36RECh-4 P-37RECh-4 P-38RECh-4 P-39RECh-4 P-43RECh-4 P-44RECh-4 P-45RECh-4 P-46RECh-4 P-47RECh-4 P-48RECh-4 P-49RECh-4 P-50RECh-4 P-51RECh-4 P-52RECh-4 P-53RECh-4 P-54RECh-4 P-55RECh-4 P-56RECh-4 P-57RECh-4 P-58RECh-4 P-59RECh-4 P-60RECh-4 P-61RECh-4 P-62RECh-4 P-63RECh-4 P-64RECh-4 P-65RECh-4 P-66RECh-4 P-67RECh-4 P-68RECh-4 P-69RECh-4 P-70RECh-4 P-71RECh-4 P-72RECh-4 P-73RECh-4 P-74RECh-4 P-75RECh-4 P-76RECh-4 P-77RECh-4 P-78RECh-4 P-79RECh-4 P-80RECh-4 P-81RECh-4 P-82RECh-4 P-83RECh-4 P-84RECh-4 P-85RECh-4 P-86RECh-4 P-1PCh-4 P-2PCh-4 P-3PCh-4 P-4PCh-4 P-5PCh-4 P-6PCh-4 P-7PCh-4 P-8PCh-4 P-9PCh-4 P-10PCh-4 P-11PCh-4 P-12PCh-4 P-13PCh-4 P-14PCh-4 P-15PCh-4 P-16PCh-4 P-17PCh-4 P-18PCh-4 P-19PCh-4 P-20PCh-4 P-21PCh-4 P-22PCh-4 P-23PCh-4 P-25PCh-4 P-26P

Additional Math Solutions

Find more solutions based on key concepts

Show solutions add

Find the mean, median, and mode for the following scores; 8, 7, 5, 7, 0, 10, 2, 4, 11, 7, 8, 7

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

In Exercises 107-120, factor each expression completely. 114. 3x2 4x 4

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

In Exercises 4 to 10, state the cardinality of each set. { x|5 x 9)

Mathematical Excursions (MindTap Course List)

In problems 13-16, Use notation to indicate which set is a subset of the other. 16.

Mathematical Applications for the Management, Life, and Social Sciences

Evaluate the definite integral. 0/6sintcos2tdt

Single Variable Calculus: Early Transcendentals

Subtract the following fractions and reduce to lowest terms. 2849145

Contemporary Mathematics for Business & Consumers

Finding a Derivative In Exercises 43-66. find the derivative of the function. g(t)=lntt2

Calculus: Early Transcendental Functions (MindTap Course List)

In Exercises 1926, pivot the system about the circled element. [1324|46]

Finite Mathematics for the Managerial, Life, and Social Sciences

In the graph at the right; limx2f(x)=. a) 2 b) 4 c) 0 d) does not exist

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

What is a ceiling effect, and how can it be a problem?

Research Methods for the Behavioral Sciences (MindTap Course List)