Question

Given the function f(x) = x^2 - 4x + 0 determine the average rate of change of the function over the interval -3 ≤ x ≤ 4

Answer 1

We are given the following function:

`f(x)=x^2-4x+0`

We are asked to determine the average rate of change in the interval:

`-3≤x≤4`

To do that we will use the following formula:

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

Where "a" and "b" are the extreme points of the interval.

Now, we substitute the value of "x = -3" in the function:

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

Solving the operations:

`f(-3)=21`

Now, we substitute "x =4":

`f(4)=(4)^2-4(4)=0`

Now, we substitute the values in the rate of change:

`r=(0-21)/(4-(-3))=-3`

Therefore, the rate of change is -3.