Single Variable Calculus: Early Tr...

8th Edition

James Stewart

ISBN: 9781305270336

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.

MathCalculusSingle Variable Calculus: Early Transcendentals8th Edition

Single Variable Calculus: Early Tr...

Solutions

Single Variable Calculus: Early Tr...

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.

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Math
Calculus Single Variable Calculus: Early Transcendentals 8th Edition

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.