# Whether the statement, if f ′ ( x ) = g ′ ( x ) for 0 &lt; x &lt; 1 then f ( x ) = g ( x ) for 0 &lt; x &lt; 1 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 7RQ
To determine

## Whether the statement, if f′(x)=g′(x) for 0<x<1 then f(x)=g(x) for 0<x<1 is true or false.

Expert Solution

### Explanation of Solution

The given statement is false.

Reason:

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

Consider the functions, f(x)=x2+1 and g(x)=x2 .

Differentiate both functions with respect to x.

f(x)=2x and g(x)=2x .

Observe that f(x)=g(x) but f(x)g(x) .

Therefore, the given statement is false.

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