Answer:
Please check the explanation.
Step-by-step explanation:
As we know that the average rate of change of f(x) in the closed
interval [a, b] is
[tex]\frac{f\left(b\right)-f\left(a\right)}{b-a}[/tex]
Given the interval [a, b] = [0, 4]
as
[tex]f(x)=2|x|[/tex]
[tex]f(b)=f(2)=2\cdot \:4[/tex] ∵ [tex]\mathrm{Apply\:absolute\:rule}:\quad \left|a\right|=a,\:a\ge 0[/tex]
[tex]= 8[/tex]
[tex]f(x)=2|x|[/tex]
[tex]f(a)=f(0)=2\cdot \:0[/tex] ∵ [tex]\mathrm{Apply\:absolute\:rule}:\quad \left|a\right|=a,\:a\ge 0[/tex]
[tex]= 0[/tex]
so the average rate of change :
[tex]\frac{f\left(b\right)-f\left(a\right)}{b-a}=\frac{8-0}{4-0}[/tex]
[tex]=\frac{8}{4}[/tex]
[tex]= 2[/tex]
We know that a rate of change basically indicates how an output quantity changes relative to the change in the input quantity. Here, it is clear the value of y increase with the increase of input.
