# Whether the statement, if f ′ ( x ) exists and non zero for all values of x then f ( 1 ) ≠ f ( 0 ) is true or false. ### 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 4, Problem 19RQ
To determine

## Whether the statement, if f′(x) exists and non zero for all values of x then f(1)≠f(0) is true or false.

Expert Solution

The given statement is true.

### Explanation of Solution

As f(x)0 there exist two cases.

Case 1:

Let f(x)>0 for all values of x .

Then the function f is strictly increasing function.

Therefore, f(1)f(0) .

Case 2:

Let f(x)<0 for all values of x .

Then the function f is strictly decreasing function.

So, f(1)f(0) .

Therefore, in both the cases f(1)f(0)

Hence the given statement is true.

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