# The differentiate quotient f ( 2 + h ) − f ( 2 ) h and simplify. ### 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 T, Problem 2CDT
To determine

## To evaluate: The differentiate quotient f(2+h)−f(2)h and simplify.

Expert Solution

The differentiate quotient f(2+h)f(2)h is 12+6h+h2.

### Explanation of Solution

Given:

The function is f(x)=x3.

Calculation:

The differentiate quotient is f(2+h)f(2)h.

Substitute x=2+h in f(x)=x3 to obtain the value of f(2+h),

f(2+h)=(2+h)3=8+12h+6h2+h3

Substitute x=2 in f(x)=x3 to obtain the value of f(2),

f(2)=(2)3=8

Substitute f(2)=8 and f(2+h)=8+12h+6h2+h3 in f(2+h)f(2)h,

8+12h+6h2+h38h=12h+6h2+h3h=12+6h+h2

Thus, the differentiate quotient f(2+h)f(2)h is 12+6h+h2.

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