BuyFindarrow_forward

Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621

Solutions

Chapter
Section
BuyFindarrow_forward

Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621
Textbook Problem

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

f ( t ) = ( t 2 4 ) 3 ,    [ 2 , 3 ]

To determine

To find:

The absolute maximum and absolute minimum values of f(x) on the given interval.

Explanation

1) Concept:

Use Closed Interval Method to find the absolute maximum and minimum values of f(x).

The Closed Interval Method:

To find the absolute maximum and minimum values of a continuous function f on a closed interval a, b:

i. Find the values of f at the critical numbers of f in a, b.

ii. Find the values of f at the end points of the interval .

iii. The largest of the values from step (i) and (ii) is the absolute maximum value; the smallest of these values is the absolute minimum value.

2) Given:

 ft= (t2-4)3, -2, 3

3) Calculation:

Since f(t) is continuous on -2, 3, use the Closed Interval Method.

Differentiate f(t) with respect to t, and then find the values of t, where f't=0 and f't doesn’t exist.

By using the chain rule of derivative,

f't=3(t2-4)2*2t

f't=6t(t2-4)2

Substitute  f't =0, and then solve for t.

0=6t(t2-4)2

Hence, t= 0, t= -2,  & t= 2

Since f't exists for all t,t= 0, t= -2, & t= 2 are the only critical points of ft

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-3.1 P-11ESect-3.1 P-12ESect-3.1 P-13ESect-3.1 P-14ESect-3.1 P-15ESect-3.1 P-16ESect-3.1 P-17ESect-3.1 P-18ESect-3.1 P-19ESect-3.1 P-20ESect-3.1 P-21ESect-3.1 P-22ESect-3.1 P-23ESect-3.1 P-24ESect-3.1 P-25ESect-3.1 P-26ESect-3.1 P-27ESect-3.1 P-28ESect-3.1 P-29ESect-3.1 P-30ESect-3.1 P-31ESect-3.1 P-32ESect-3.1 P-33ESect-3.1 P-34ESect-3.1 P-35ESect-3.1 P-36ESect-3.1 P-37ESect-3.1 P-38ESect-3.1 P-39ESect-3.1 P-40ESect-3.1 P-41ESect-3.1 P-42ESect-3.1 P-43ESect-3.1 P-44ESect-3.1 P-45ESect-3.1 P-46ESect-3.1 P-47ESect-3.1 P-48ESect-3.1 P-49ESect-3.1 P-50ESect-3.1 P-51ESect-3.1 P-52ESect-3.1 P-53ESect-3.1 P-54ESect-3.1 P-55ESect-3.1 P-56ESect-3.1 P-57ESect-3.1 P-58ESect-3.1 P-59ESect-3.1 P-60ESect-3.1 P-61ESect-3.1 P-62ESect-3.1 P-63ESect-3.1 P-64ESect-3.1 P-65ESect-3.1 P-66ESect-3.1 P-67ESect-3.1 P-68ESect-3.1 P-69ESect-3.1 P-70ESect-3.1 P-71ESect-3.1 P-72ESect-3.2 P-1ESect-3.2 P-2ESect-3.2 P-3ESect-3.2 P-4ESect-3.2 P-5ESect-3.2 P-6ESect-3.2 P-7ESect-3.2 P-8ESect-3.2 P-9ESect-3.2 P-10ESect-3.2 P-11ESect-3.2 P-12ESect-3.2 P-13ESect-3.2 P-14ESect-3.2 P-15ESect-3.2 P-16ESect-3.2 P-17ESect-3.2 P-18ESect-3.2 P-19ESect-3.2 P-20ESect-3.2 P-21ESect-3.2 P-22ESect-3.2 P-23ESect-3.2 P-24ESect-3.2 P-25ESect-3.2 P-26ESect-3.2 P-27ESect-3.2 P-28ESect-3.2 P-29ESect-3.2 P-30ESect-3.2 P-31ESect-3.2 P-32ESect-3.2 P-33ESect-3.2 P-34ESect-3.2 P-35ESect-3.2 P-36ESect-3.3 P-1ESect-3.3 P-2ESect-3.3 P-3ESect-3.3 P-4ESect-3.3 P-5ESect-3.3 P-6ESect-3.3 P-7ESect-3.3 P-8ESect-3.3 P-9ESect-3.3 P-10ESect-3.3 P-11ESect-3.3 P-12ESect-3.3 P-13ESect-3.3 P-14ESect-3.3 P-15ESect-3.3 P-16ESect-3.3 P-17ESect-3.3 P-18ESect-3.3 P-19ESect-3.3 P-20ESect-3.3 P-21ESect-3.3 P-22ESect-3.3 P-23ESect-3.3 P-24ESect-3.3 P-25ESect-3.3 P-26ESect-3.3 P-27ESect-3.3 P-28ESect-3.3 P-29ESect-3.3 P-30ESect-3.3 P-31ESect-3.3 P-32ESect-3.3 P-33ESect-3.3 P-34ESect-3.3 P-35ESect-3.3 P-36ESect-3.3 P-37ESect-3.3 P-38ESect-3.3 P-39ESect-3.3 P-40ESect-3.3 P-41ESect-3.3 P-42ESect-3.3 P-43ESect-3.3 P-44ESect-3.3 P-45ESect-3.3 P-46ESect-3.3 P-47ESect-3.3 P-48ESect-3.3 P-49ESect-3.3 P-50ESect-3.3 P-51ESect-3.3 P-52ESect-3.3 P-53ESect-3.3 P-54ESect-3.3 P-55ESect-3.3 P-56ESect-3.3 P-57ESect-3.3 P-58ESect-3.3 P-59ESect-3.3 P-60ESect-3.3 P-61ESect-3.3 P-62ESect-3.3 P-63ESect-3.3 P-64ESect-3.3 P-65ESect-3.3 P-66ESect-3.3 P-67ESect-3.3 P-68ESect-3.3 P-69ESect-3.3 P-70ESect-3.3 P-71ESect-3.3 P-72ESect-3.3 P-73ESect-3.3 P-74ESect-3.3 P-75ESect-3.3 P-76ESect-3.3 P-77ESect-3.4 P-1ESect-3.4 P-2ESect-3.4 P-3ESect-3.4 P-4ESect-3.4 P-5ESect-3.4 P-6ESect-3.4 P-7ESect-3.4 P-8ESect-3.4 P-9ESect-3.4 P-10ESect-3.4 P-11ESect-3.4 P-12ESect-3.4 P-13ESect-3.4 P-14ESect-3.4 P-15ESect-3.4 P-16ESect-3.4 P-17ESect-3.4 P-18ESect-3.4 P-19ESect-3.4 P-20ESect-3.4 P-21ESect-3.4 P-22ESect-3.4 P-23ESect-3.4 P-24ESect-3.4 P-25ESect-3.4 P-26ESect-3.4 P-27ESect-3.4 P-28ESect-3.4 P-29ESect-3.4 P-30ESect-3.4 P-31ESect-3.4 P-32ESect-3.4 P-33ESect-3.4 P-34ESect-3.4 P-35ESect-3.4 P-36ESect-3.4 P-37ESect-3.4 P-38ESect-3.4 P-39ESect-3.4 P-40ESect-3.4 P-41ESect-3.4 P-42ESect-3.4 P-43ESect-3.4 P-44ESect-3.4 P-45ESect-3.4 P-46ESect-3.4 P-47ESect-3.4 P-48ESect-3.4 P-49ESect-3.4 P-50ESect-3.4 P-51ESect-3.4 P-52ESect-3.4 P-53ESect-3.4 P-54ESect-3.4 P-55ESect-3.4 P-56ESect-3.4 P-57ESect-3.4 P-58ESect-3.4 P-59ESect-3.4 P-60ESect-3.4 P-61ESect-3.4 P-62ESect-3.4 P-63ESect-3.4 P-64ESect-3.4 P-65ESect-3.4 P-66ESect-3.4 P-67ESect-3.4 P-68ESect-3.4 P-69ESect-3.4 P-70ESect-3.4 P-71ESect-3.4 P-72ESect-3.4 P-73ESect-3.4 P-74ESect-3.5 P-1ESect-3.5 P-2ESect-3.5 P-3ESect-3.5 P-4ESect-3.5 P-5ESect-3.5 P-6ESect-3.5 P-7ESect-3.5 P-8ESect-3.5 P-9ESect-3.5 P-10ESect-3.5 P-11ESect-3.5 P-12ESect-3.5 P-13ESect-3.5 P-14ESect-3.5 P-15ESect-3.5 P-16ESect-3.5 P-17ESect-3.5 P-18ESect-3.5 P-19ESect-3.5 P-20ESect-3.5 P-21ESect-3.5 P-22ESect-3.5 P-23ESect-3.5 P-24ESect-3.5 P-25ESect-3.5 P-26ESect-3.5 P-27ESect-3.5 P-28ESect-3.5 P-29ESect-3.5 P-30ESect-3.5 P-31ESect-3.5 P-32ESect-3.5 P-33ESect-3.5 P-34ESect-3.5 P-35ESect-3.5 P-36ESect-3.5 P-37ESect-3.5 P-38ESect-3.5 P-39ESect-3.5 P-40ESect-3.5 P-41ESect-3.5 P-42ESect-3.5 P-43ESect-3.5 P-44ESect-3.5 P-45ESect-3.5 P-46ESect-3.5 P-47ESect-3.5 P-48ESect-3.5 P-49ESect-3.5 P-50ESect-3.5 P-51ESect-3.5 P-52ESect-3.5 P-53ESect-3.5 P-54ESect-3.5 P-55ESect-3.5 P-56ESect-3.5 P-57ESect-3.5 P-58ESect-3.5 P-59ESect-3.5 P-60ESect-3.6 P-1ESect-3.6 P-2ESect-3.6 P-3ESect-3.6 P-4ESect-3.6 P-5ESect-3.6 P-6ESect-3.6 P-7ESect-3.6 P-8ESect-3.6 P-9ESect-3.6 P-10ESect-3.6 P-11ESect-3.6 P-12ESect-3.6 P-13ESect-3.6 P-14ESect-3.6 P-15ESect-3.6 P-16ESect-3.6 P-17ESect-3.6 P-18ESect-3.6 P-19ESect-3.6 P-20ESect-3.6 P-21ESect-3.6 P-22ESect-3.6 P-23ESect-3.6 P-24ESect-3.6 P-25ESect-3.6 P-26ESect-3.6 P-27ESect-3.6 P-28ESect-3.7 P-1ESect-3.7 P-2ESect-3.7 P-3ESect-3.7 P-4ESect-3.7 P-5ESect-3.7 P-6ESect-3.7 P-7ESect-3.7 P-8ESect-3.7 P-9ESect-3.7 P-10ESect-3.7 P-11ESect-3.7 P-12ESect-3.7 P-13ESect-3.7 P-14ESect-3.7 P-15ESect-3.7 P-16ESect-3.7 P-17ESect-3.7 P-18ESect-3.7 P-19ESect-3.7 P-20ESect-3.7 P-21ESect-3.7 P-22ESect-3.7 P-23ESect-3.7 P-24ESect-3.7 P-25ESect-3.7 P-26ESect-3.7 P-27ESect-3.7 P-28ESect-3.7 P-29ESect-3.7 P-30ESect-3.7 P-31ESect-3.7 P-32ESect-3.7 P-33ESect-3.7 P-34ESect-3.7 P-35ESect-3.7 P-36ESect-3.7 P-37ESect-3.7 P-38ESect-3.7 P-39ESect-3.7 P-40ESect-3.7 P-41ESect-3.7 P-42ESect-3.7 P-43ESect-3.7 P-44ESect-3.7 P-45ESect-3.7 P-46ESect-3.7 P-47ESect-3.7 P-48ESect-3.7 P-49ESect-3.7 P-50ESect-3.7 P-51ESect-3.7 P-52ESect-3.7 P-53ESect-3.7 P-54ESect-3.7 P-55ESect-3.7 P-56ESect-3.7 P-57ESect-3.7 P-58ESect-3.7 P-59ESect-3.7 P-60ESect-3.7 P-61ESect-3.7 P-62ESect-3.7 P-63ESect-3.7 P-64ESect-3.7 P-65ESect-3.7 P-66ESect-3.7 P-67ESect-3.7 P-68ESect-3.7 P-69ESect-3.7 P-70ESect-3.7 P-71ESect-3.7 P-72ESect-3.7 P-73ESect-3.7 P-74ESect-3.7 P-75ESect-3.7 P-76ESect-3.7 P-77ESect-3.7 P-78ESect-3.7 P-79ESect-3.7 P-80ESect-3.8 P-1ESect-3.8 P-2ESect-3.8 P-3ESect-3.8 P-4ESect-3.8 P-5ESect-3.8 P-6ESect-3.8 P-7ESect-3.8 P-8ESect-3.8 P-9ESect-3.8 P-10ESect-3.8 P-11ESect-3.8 P-12ESect-3.8 P-13ESect-3.8 P-14ESect-3.8 P-15ESect-3.8 P-16ESect-3.8 P-17ESect-3.8 P-18ESect-3.8 P-19ESect-3.8 P-20ESect-3.8 P-21ESect-3.8 P-22ESect-3.8 P-23ESect-3.8 P-24ESect-3.8 P-25ESect-3.8 P-26ESect-3.8 P-27ESect-3.8 P-28ESect-3.8 P-29ESect-3.8 P-30ESect-3.8 P-31ESect-3.8 P-32ESect-3.8 P-33ESect-3.8 P-34ESect-3.8 P-35ESect-3.8 P-36ESect-3.8 P-37ESect-3.8 P-38ESect-3.8 P-39ESect-3.8 P-40ESect-3.9 P-1ESect-3.9 P-2ESect-3.9 P-3ESect-3.9 P-4ESect-3.9 P-5ESect-3.9 P-6ESect-3.9 P-7ESect-3.9 P-8ESect-3.9 P-9ESect-3.9 P-10ESect-3.9 P-11ESect-3.9 P-12ESect-3.9 P-13ESect-3.9 P-14ESect-3.9 P-15ESect-3.9 P-16ESect-3.9 P-17ESect-3.9 P-18ESect-3.9 P-19ESect-3.9 P-20ESect-3.9 P-21ESect-3.9 P-22ESect-3.9 P-23ESect-3.9 P-24ESect-3.9 P-25ESect-3.9 P-26ESect-3.9 P-27ESect-3.9 P-28ESect-3.9 P-29ESect-3.9 P-30ESect-3.9 P-31ESect-3.9 P-32ESect-3.9 P-33ESect-3.9 P-34ESect-3.9 P-35ESect-3.9 P-36ESect-3.9 P-37ESect-3.9 P-38ESect-3.9 P-39ESect-3.9 P-40ESect-3.9 P-41ESect-3.9 P-42ESect-3.9 P-43ESect-3.9 P-44ESect-3.9 P-45ESect-3.9 P-46ESect-3.9 P-47ESect-3.9 P-48ESect-3.9 P-49ESect-3.9 P-50ESect-3.9 P-51ESect-3.9 P-52ESect-3.9 P-53ESect-3.9 P-54ESect-3.9 P-55ESect-3.9 P-56ESect-3.9 P-57ESect-3.9 P-58ESect-3.9 P-59ESect-3.9 P-60ESect-3.9 P-61ESect-3.9 P-62ESect-3.9 P-63ESect-3.9 P-64ESect-3.9 P-65ESect-3.9 P-66ESect-3.9 P-67ESect-3.9 P-68ESect-3.9 P-69ESect-3.9 P-70ESect-3.9 P-71ESect-3.9 P-72ESect-3.9 P-73ESect-3.R P-1CCSect-3.R P-2CCSect-3.R P-3CCSect-3.R P-4CCSect-3.R P-5CCSect-3.R P-6CCSect-3.R P-7CCSect-3.R P-8CCSect-3.R P-9CCSect-3.R P-10CCSect-3.R P-11CCSect-3.R P-1TFQSect-3.R P-2TFQSect-3.R P-3TFQSect-3.R P-4TFQSect-3.R P-5TFQSect-3.R P-6TFQSect-3.R P-7TFQSect-3.R P-8TFQSect-3.R P-9TFQSect-3.R P-10TFQSect-3.R P-11TFQSect-3.R P-12TFQSect-3.R P-13TFQSect-3.R P-14TFQSect-3.R P-15TFQSect-3.R P-16TFQSect-3.R P-17TFQSect-3.R P-18TFQSect-3.R P-19TFQSect-3.R P-1ESect-3.R P-2ESect-3.R P-3ESect-3.R P-4ESect-3.R P-5ESect-3.R P-6ESect-3.R P-7ESect-3.R P-8ESect-3.R P-9ESect-3.R P-10ESect-3.R P-11ESect-3.R P-12ESect-3.R P-13ESect-3.R P-14ESect-3.R P-15ESect-3.R P-16ESect-3.R P-17ESect-3.R P-18ESect-3.R P-19ESect-3.R P-20ESect-3.R P-21ESect-3.R P-22ESect-3.R P-23ESect-3.R P-24ESect-3.R P-25ESect-3.R P-26ESect-3.R P-27ESect-3.R P-28ESect-3.R P-29ESect-3.R P-30ESect-3.R P-31ESect-3.R P-32ESect-3.R P-33ESect-3.R P-34ESect-3.R P-35ESect-3.R P-36ESect-3.R P-37ESect-3.R P-38ESect-3.R P-39ESect-3.R P-40ESect-3.R P-41ESect-3.R P-42ESect-3.R P-43ESect-3.R P-44ESect-3.R P-45ESect-3.R P-46ESect-3.R P-47ESect-3.R P-48ESect-3.R P-49ESect-3.R P-50ESect-3.R P-51ESect-3.R P-52ESect-3.R P-53ESect-3.R P-54ESect-3.R P-55ESect-3.R P-56ESect-3.R P-57ESect-3.R P-58ESect-3.R P-59ESect-3.R P-60ESect-3.R P-61ESect-3.R P-62ESect-3.R P-63ESect-3.R P-64ESect-3.R P-65ESect-3.R P-66ESect-3.R P-67ESect-3.R P-68ESect-3.P P-1PSect-3.P P-2PSect-3.P P-3PSect-3.P P-4PSect-3.P P-5PSect-3.P P-6PSect-3.P P-7PSect-3.P P-8PSect-3.P P-9PSect-3.P P-10PSect-3.P P-11PSect-3.P P-12PSect-3.P P-13PSect-3.P P-14PSect-3.P P-15PSect-3.P P-16PSect-3.P P-17PSect-3.P P-18PSect-3.P P-19PSect-3.P P-20PSect-3.P P-21PSect-3.P P-22PSect-3.P P-23PSect-3.P P-24P

Additional Math Solutions

Find more solutions based on key concepts

Show solutions add

Solve the equations in Exercises 126. (x2+1)x+1(x+1)3=0

Finite Mathematics and Applied Calculus (MindTap Course List)

Evaluate the integral. 55edx

Single Variable Calculus: Early Transcendentals, Volume I

For the following set of stores, find the value of each expression: a. X b. (X) c. (X 3) d. (X 3) X 4 5 2 1 3

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

Define (a) a polynomial function and (b) a rational function. Give an example of each.

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

Evaluate the definite integrals in Problems 1-32. 28.

Mathematical Applications for the Management, Life, and Social Sciences

Add the following fractions and reduce to lowest terms. 58+1316

Contemporary Mathematics for Business & Consumers

How fast is the angle between the hands of an analog clock increasing at 3:30 pm? 2π radians/hr

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