# The average rate of change of function f ( x ) = x 2 between x = 1 and x = 5 .

### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

#### Solutions

Chapter 2.4, Problem 3E
To determine

## To fill: The average rate of change of function f(x)=x2 between x=1 and x=5 .

Expert Solution

The average rate of change is 25151=6 .

### Explanation of Solution

Given:

The given function is,

f(x)=x2 (1)

The average rate of change of a function is the slope of the scant line between the x=a and x=b .

Average rate of change of function y=f(x) between. x=a and x=b .

Averagerateofchange=ChangeinyChangeinx=f(b)f(a)ba (2)

Substitute 1 for a and 5 for b in equation (2)

Averagerateofchange=f(5)f(1)51 (3)

For f(5) substitute 5 for x in equation (1)

f(5)=(5)2=25

For f(1) substitute 1 for x in equation (1)

f(1)=(1)2=1

Again substitute 25 for f(5) and 1 for f(1) in equation (3).

Averagerateofchange=25151=244=6

Thus, the average rate of change is 25151=6 .

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