Question

Consider the function given by f(x)= x² +3. Find its average rate of change from x = -2 to x = 4.

Carefully show the work that leads to your final answer.

Answer 1

`Rate = 2`

Explanation:

Given

`f(x) = x^2 + 3`

Required

Determine the average rate of change from -2 to 4

This is calculated using:

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

In this case:

`a = -2`

`b = 4`

So, we have:

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

`Rate = (f(4) - f(-2))/(4 - (-2))`

`Rate = (f(4) - f(-2))/(4 +2)`

`Rate = (f(4) - f(-2))/(6)`

Calculate f(4):

`f(x) = x^2 + 3`

`f(4) = 4^2 + 3`

`f(4) = 19`

Calculate f(-2)

`f(x) = x^2 + 3`

`f(-2) = (-2)^2 + 3`

`f(-2) = 7`

So:

`Rate = (f(4) - f(-2))/(6)`

`Rate = (19-7)/(6)`

`Rate = (12)/(6)`

`Rate = 2`

The average rate of change is 2.