# The difference quotient f ( a + h ) − f ( a ) h of the function f ( x ) = x 2 − 2 x + 3 .

### 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, Problem 3RE
To determine

## The difference quotient f(a+h)−f(a)h of the function f(x)=x2−2x+3.

Expert Solution

The difference quotient of the function f (x) is 2a+h2.

### Explanation of Solution

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

f(1)=a22a+3

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

f(a+h)=(a+h)22(a+h)+3=a2+2ah+h22a2h+3

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

f(a+h)f(a)h=a2+2ah+h22a2h+3a2+2a3h=2ah+h22hh=h(2a+h2)h=2a+h2

Therefore, the difference quotient of the function is 2a+h2.

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