We are given the following function:
[tex]f(x)=x^2-4x+0[/tex]We are asked to determine the average rate of change in the interval:
[tex]-3≤x≤4[/tex]To do that we will use the following formula:
[tex]r=\frac{f(b)-f(a)}{b-a}[/tex]Where "a" and "b" are the extreme points of the interval.
Now, we substitute the value of "x = -3" in the function:
[tex]f(-3)=(-3)^2-4(-3)[/tex]Solving the operations:
[tex]f(-3)=21[/tex]Now, we substitute "x =4":
[tex]f(4)=(4)^2-4(4)=0[/tex]Now, we substitute the values in the rate of change:
[tex]r=\frac{0-21}{4-(-3)}=-3[/tex]Therefore, the rate of change is -3.
