# the average rate of change of the function.

### 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 19E
To determine

## To find: the average rate of change of the function.

Expert Solution

The average rate of change of the function is 2a(a+h)

### Explanation of Solution

Given information:

The function is f(t)=2t and value of the variables is t=a and t=a+h

Formula used:

The average rate of change of the function is f(x2)f(x1)f2f1

Calculation:

Substitution of f(a) and f(a+h)

f(a)=2af(a+h)=2a+h

Therefore, the average rate of change on the indicated interval will be:

f(a+h)f(a)(a+h)a=2a+h2aa+ha                   =2a2(a+h)a(a+h)h                          [simplify]                   =2a2a2ha(a+h)h                [simply]                   =2ha(a+h)h                   =2hha(a+h)            [cancel any common factors]                   =2a(a+h)

Hence, the average rate of change of the function is 2a(a+h)

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