Question

!!time sensitive!!

Given the function f(x) = 72 - 6x + 6, determine the average rate of change of
the function over the interval 2 < x < 8.


Answer 1

The average rate of change is 64

Explanation:

Given

`f(x) = 7x^2 - 6x + 6`

Required'

Average rate over 2 < x < 8

The average rate of change is calculated as:

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

Where a < x < b

So, we have:

`Rate = (f(8) - f(2))/(8-2)`

`Rate = (f(8) - f(2))/(6)`

Calculate f(8) and f(2)

`f(x) = 7x^2 - 6x + 6`

`f(8) = 7 * 8^2-6 * 8 +6 = 406`

`f(2) = 7 * 2^2-6 * 2 +6 = 22`

So:

`Rate = (f(8) - f(2))/(6)`

`Rate = (406 - 22)/(6)`

`Rate = (384)/(6)`

`Rate = 64`