   Chapter 2.5, Problem 50E ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

#### Solutions

Chapter
Section ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

# Suppose that a function f is continuous on [0, 1] except at 0.25 and that f(0) = 1 and f(l) = 3. Let N = 2. Sketch two possible graphs of f, one showing that f might not satisfy the conclusion of the Intermediate Value Theorem and one showing that f might still satisfy the conclusion of the Intermediate Value Theorem (even though it doesn’t satisfy the hypothesis).

To determine

To sketch: The graph of f(x) which might not satisfy the conclusion of Intermediate Value Theorem.

Explanation

Given:

A function f(x) is continuous on the interval [0,1] except at x=0.25 and also f(0)=1, f(1)=3 and also let N=2.

Intermediate Value Theorem:

“Suppose that f is continuous on the closed interval [a,b] and let N be any number between f(a) and f(b), where f(a)f(b). Then, there exists a number c in (a,b) such that f(c)=N”.

The graph of the function f(x) does not satisfy the conclusion of Intermediate Value Theorem as shown below in Figure 1.

From Figure (1), it is observed that f(x) does not satisfies the hypothesis of the Intermediate value Theorem. That is, the function f is continuous on the closed interval [0,1] except at x=0.25.

Choose N=2 which lies between f(0) and f(1), where f(0)f(1). But there is no number c in (0,1) such that f(c)=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

#### In Exercises 1-6, simplify the expression. 1. x2+x2x24

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

#### Perform the indicated operations and simplify.

Mathematical Applications for the Management, Life, and Social Sciences

#### True or False: n=21(lnn)n converges.

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

#### Define the validity of measurement and explain why and how it is measured.

Research Methods for the Behavioral Sciences (MindTap Course List) 