# The average rate of change of f between x = 0 and x = 2 . Also, the average rate of change of f between x = 15 and x = 50 .

### 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, Problem 62RE

(a)

To determine

## To find: The average rate of change of f between x=0 and x=2 . Also, the average rate of change of f between x=15 and x=50 .

Expert Solution

The average rate of change of f between x=0 and x=2 is equal to 3 . The average rate of change of f between x=15 and x=50 is equal to 3 .

### Explanation of Solution

Given information:

The function is f(x)=83x .

Calculation:

The formula for average rate of change f(x) between x=a and x=b is equal to f(b)f(a)ba .

Substitute 0 for x in the function.

f(x)=83xf(0)=83×0f(0)=80f(0)=8

Substitute 2 for x in the function.

f(x)=83xf(2)=83×2f(2)=86f(2)=2

Substitute 0 for a , 2 for b , 8 for f(0) and 2 for f(2) in the formula.

f(b)f(a)ba=f(2)f(0)20=282=62=3

So, the average rate of change of f between x=0 and x=2 is equal to 3 .

Substitute 15 for x in the function.

f(x)=83xf(15)=83×15f(15)=845f(15)=37

Substitute 50 for x in the function.

f(x)=83xf(50)=83×50f(50)=8150f(50)=142

Substitute 15 for a , 50 for b , 37 for f(15) and 142 for f(50) in the formula.

f(b)f(a)ba=f(50)f(15)5015=142(37)35=10535=3

So, the average rate of change of f between x=15 and x=50 is equal to 3 .

Therefore, the average rate of change of f between x=0 and x=2 is equal to 3 . The average rate of change of f between x=15 and x=50 is equal to 3 .

(b)

To determine

### To check: Whether the two average rate of change in part(a) is same or not explain.

Expert Solution

The two average rate of change in part (a) are same as the function is linear polynomial function, it varies linearly so the average rate of change is same.

### Explanation of Solution

Given information:

The function is f(x)=83x .

As calculated in part(a), the value of average rate of change for both is equal to 3 .

The given function f(x)=83x is linear polynomial and it varies linearly. So, the average rate of change for the function for any two values of x is same.

Therefore, the two average rate of change in part (a) are same.

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