# 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 25E
To determine

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

Expert Solution

The answerof the function is, (h3)

### Explanation of Solution

Given information:

The given function is,

f(x)=4+3xx2

Andthisevaluation of the quotient is f(3+h)f(3)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)=4+3xx2

And evaluate this f(3+h)f(3)h for the function.

Now we calculate (3+h) for x in the given function f(x)=4+3xx2 ,

f(3+h)=4+3(3+h)(3+h)2=13+3h(9+h2+6h)=13+3h9h26h=h23h+4

Now, calculate f(3)

f(3)=4+3(3)(3)2=4+99=4

All values of f(3+h) and f(3) stand in f(3+h)f(3)h

f(3+h)f(3)h=h23h+44h=h23hh=h(h+3)h=h3

Therefore, the answer of the function is (h3) .

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