Question

What is the average rate of change for this function for the interval from x=3 to x=5?​

Answer 1

The average rate of change is
`12`

Explanation:

Given:

Interval; x = 3 to x = 5

We'll represent these by

x1 = 3

x2 = 5

The corresponding y values are:

When x = 3, y = 8

When x = 5, y = 32

This will also be represented

y1 = 8

y2 = 32

Average rate of change is then calculated as follows

`m = (y_(2) - y_(1))/(x_(2) - x_(1))`

Where m represent average rate of change

By Substitution, we have

`m = (32 - 8)/(5 - 3)`

`m = (24)/(2)`

`m = 12`

Hence, the average rate of change is
`12`

Answer 2

B

Explanation:

The average rate of change of f(x) in the closed interval [ a, b ] is

`(f(b)-f(a))/(b-a)`

Here [ a, b ] = [ 3, 5 ]

From the table of values

f(b) = f(5) = 32

f(a) = f(3) = 8

Hence

average rate of change =
`(32-8)/(5-3)` =
`(24)/(2)` = 12