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4th Edition

James Stewart

Publisher: Cengage Learning

ISBN: 9781337687805

Chapter 2, Problem 12RQ

To determine

Whether the statement, “If *c* between 1 and 3 such that

Expert Solution

The statement is false.

**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 *c* in (*a*, *b*) such that

**Reason:**

The given statement is false since the below example disproves the given statement.

Suppose

Here,

This implies that,

Suppose the function

**At the interval (1, 2):**

Suppose the function *c* in the interval (1, 2), then

**At the interval (2, 3):**

Suppose the function *c* in the interval (2, 3), then

**At the point** **:**

Suppose the function

It is clear that from the above subintervals, there is no *c* between 1 and 3 for which

Even though *c* between 1 and 3 for which

Therefore, the statement is false.