Question

Find the average rate of change of f(x) = x² - 4x + 1 from x=3 to x = 5.

Simplify your answer as much as possible.

Answer 1

Explanation:

Given a interval x=a to x=b, the average rate of change is equal to

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

where [a,b] is the interval.

Here

a is 3

b is 5 so

`(f(5) - f(3))/(5 - 3)`

Using the function

`f(5) = 25 - 20 + 1 = 6`

`f(3) = 9 - 12 + 1 = - 2`

So

`(6 - ( - 2))/(5 - 3) = 4`

The average rate of change of f from x=3 to x=5 is 4

Answer 2

To find the average rate of change of the function f(x) = x² - 4x + 1 from x=3 to x = 5, we need to find the difference in f(x) between these two values and divide by the difference in x:

f(5) - f(3) / (5 - 3)

= (5² - 4(5) + 1) - (3² - 4(3) + 1) / 2

= (25 - 20 + 1) - (9 - 12 + 1) / 2

= (6) / 2

= 3

Therefore, the average rate of change of f(x) from x=3 to x=5 is 3.