# the difference quotient for the given function.

### 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 1.1, Problem 26E
To determine

## To find: the difference quotient for the given function.

Expert Solution

The answerof the function is, (h2+3ah+3a2)

### Explanation of Solution

Given information:

The given function is,

f(x)=x3

Andthisevaluation of the quotient is f(a+h)f(a)h for the function.

Concept used:

To represent the function:

A function f is a rule that assigns to each element x in a set D exactly one element called f(x) in a set E

The given function is

f(x)=x3

And evaluate this f(a+h)f(a)h for the function.

Now we calculate (a+h) for x in the given function f(x)=x3 ,

f(a+h)=(a+h)3=a3+h3+3ah(a+h)=a3+h3+3a2h+3ah2

Now calculate f(a)

f(a)=a3

All values of f(a+h) and f(a) stand in f(a+h)f(a)h

f(a+h)f(a)h=a3+h3+3a2h+3ah2a3h=h3+3a2h+3ah2h=h(h2+3a2+3ah)h=h2+3a2+3ah

Therefore,the answer of the function is, (h2+3ah+3a2) .

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