Answer:
Therefore, the average rate of change is 2.
Step-by-step explanation:
The average rate of change of for [tex]f(x) = 2x - 12[/tex] over the interval [tex]4 \leq x \leq 8[/tex] will be the slope of the secant line connecting the 2 points.
To calculate the average rate of change of f(x) on the interval [a, b] is:
[tex]\frac{f\left(b\right)-f\left(a\right)}{b-a}[/tex]
as
[tex]f\left(4\right)\:=\:2\left(4\right)\:-\:12[/tex]
[tex]=-4[/tex]
[tex]f\left(8\right)\:=\:2\left(8\right)\:-\:12[/tex]
[tex]=16-12[/tex]
[tex]=4[/tex]
The average rate of change between (4, -4) and (8, 4) will be:
[tex]\frac{f\left(b\right)-f\left(a\right)}{b-a}[/tex]
[tex]=\frac{4-\left(-4\right)}{8-4}[/tex]
[tex]=\frac{4+4}{8-4}[/tex]
[tex]=\frac{8}{4}[/tex]
[tex]=2[/tex]
Therefore, the average rate of change is 2.
