   Chapter 2, Problem 18RQ

Chapter
Section
Textbook Problem

Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement.If f is continuous on [ –1 , 1] and f(–1) = 4 and f(1) = 3, then there exists. a number r such that | r | < 1 and f(r) = π.

To determine

Whether the statement, “If f is continuous on [1,1] and f(1)=4 and f(1)=3, then there exists a number r such that |r|<1 and f(r)=π” is true or false.

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.

Reason:

Suppose f is continuous on [1,1] and f(1)=4 and f(1)=3

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