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

11-14 Verify that the function satisfies the hypotheses of the Mean Value Theorem on the given interval. Then find all numbers c that satisfy the conclusion of the Mean Value Theorem.

f ( x ) = 2 x 2 3 x + 1 ,    [ 0 , 2 ]

To determine

To verify:

(i) Whether the function satisfies the hypothesis of Mean Value Theorem on the given interval.

(ii) Find all numbers c that satisfy the conclusion of Mean Value theorem.

Explanation

1) Concept:

Using the Mean Value Theorem verify the result and find all the values of c

2) Theorem:

Mean value theorem- Let f be a function that satisfies the following hypotheses:(i) f is continuous on the closed interval [a, b].(ii) f is differentiable on the open interval (a, b). Then there is a number c in (a, b) such that f'c=fb -f(a)b - a or equivalently, f(b)  f(a) = f(c) (b  a).

3) Given:

fx=2x2-3x+1, [0, 2]

4) Calculations:

(i) Consider the given function fx=2x2-3x+1

As a polynomial function is always continuous and differentiable everywhere

Therefore, f(x) is continuous on [0, 2] and differentiable on (0, 2).

Hence, it satisfies hypothesis of Mean Value Theorem.

(ii) By using Mean Value theorem, as f(x) is continuous on [0, 2] and differentiable on (0, 2)

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

A sample of n = 9 scores has X = 108. What is the sample mean?

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

Find an equation of the line that passes through (1, 2) and (4, 5).

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

Evaluate each expression: 32+12323

Elementary Technical Mathematics

In the graph at the right, limx1f(x)=. a) 2 b) 1 c) 3 d) does not exist

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

In the figure, mEFG=68 and m3=33. Find m4.________

Elementary Geometry for College Students

Explain how the enforcement of confidentiality benefits both the participants and the researcher.

Research Methods for the Behavioral Sciences (MindTap Course List)

Solve for x. 30. logx72=2

College Algebra (MindTap Course List)