Answer:
The average rate of change of the function [tex]f(x)[/tex] from [tex]x=0[/tex] to [tex]x=2[/tex] is equal to 6.
Step-by-step explanation:
Let's define the average rate of change of the function [tex]f(x)[/tex] over the interval [a,b] :
[tex]A(x)=[/tex] Δf / Δx = [tex]\frac{f(b)-f(a)}{b-a}[/tex]
In the exercise, [tex]a=0[/tex] and [tex]b=2[/tex]
Now we calculate [tex]f(a)[/tex] and [tex]f(b)[/tex]
[tex]f(a)=f(0)=4.(2^{0})=4.1=4[/tex]
[tex]f(b)=f(2)=4.(2^{2})=(4).(4)=16[/tex]
⇒ [tex]f(b)-f(a)=16-4=12[/tex] and [tex]b-a=2-0=2[/tex]
Finally, the average rate of change is
[tex]\frac{f(b)-f(a)}{b-a}=\frac{12}{2}=6[/tex]
