   Chapter 1.1, Problem 28E ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

#### Solutions

Chapter
Section ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

# Evaluate the difference quotient for the given function. Simplify your answer.28. f ( x ) = x 3 ,   f ( a + h ) − f ( a ) h

To determine

To find: The difference quotient f(a+h)f(a)h of the function f(x)=x3 .

Explanation

Given:

The function f(x)=x3 .

Calculation:

Find f(a) , replacing x by a in the expression for f(x) .

f(a)=a3

Evaluate f(a+h) , replacing x by a + h in the expression for f(x) .

f(a+h)=(a+h)3=a3+3a2h+3ah2+h3          [Since (a+b)3=a3+3a2b+3ab2+b3]

Substitute f(a) and f(a+h) into the difference quotient expression and simplify

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