   Chapter 2.5, Problem 52E

Chapter
Section
Textbook Problem

Suppose f is continuous on [1, 5] and the only solutions of the equation f(x) = 6 arc x = 1 and x = 4.lf f(2) = 8, explain why f(3) > 6.

To determine

To explain: Why f(3)>6 if f(2)=8 and f is continuous on [1,5] and the only solutions of the equation f(x)=6 are x=1 and x=4.

Explanation

Theorem used: The Intermediate value Theorem

Suppose that if 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.

Calculation:

Suppose f(3)<6.

Given that, f(2)=8>6.

The function f is continuous on the interval [1,2] because f is continuous on [1,5].

This implies that, f(3)<6<f(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

What is the lowest score in the following distribution?

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

In Problems 29-32, use algebra to rewrite the integrands; then integrate and simplify. 29.

Mathematical Applications for the Management, Life, and Social Sciences

True or False: If converges and converges, then converges.

Study Guide for Stewart's Multivariable Calculus, 8th

limx2x2(x1)1x = _____. a) 4 b) 1 c) 0 d) does not exist

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