# The meaning of the intermediate value theorem.

### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

#### Solutions

Chapter 2, Problem 8RCC
To determine

## To find:The meaning of the intermediate value theorem.

Expert Solution

The intermediate value theorem is explained.

### Explanation of Solution

Given information:

The intermediate value theorem.

Calculation:

Let’s 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 exist a number c in (a,b) , such that f(c)=N .

The intermediate value theorem states that a condition function takes on every intermediate value between the function values f(a) and f(b) . Note that the value N can be taken on once or more than once intermediate value theorem is true for continuous function and it is not true for discontinuous functions.

Therefore, the intermediate value theorem is explained.

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