# Thefunction f and a number a . ### 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 32RE
To determine

## To find:Thefunction f and a number a .

Expert Solution

The function f is f(x)=x6 and 2 is the correct number.

### Explanation of Solution

Given information:

The given function is limh0(2+h)664h=f'(a)

Calculation:

Using the function.

limh0(2+h)664h=f'(a)

The derivative of a function f at a point a is defined by.

f'(a)=limh0(a+h)f(a)h

Equate f'(a) from above equations.

limh0(2+h)664h=limh0(a+h)f(a)h

2 is being added to h inside of a function, 2 is the natural choice for a .

f(2+h)=(2+h)6

The suitable choice for f is.

f(x)=x6f(2)=26=64

Therefore, the function f is f(x)=x6 and 2 is the correct number.

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