Answer:
Average rate of change= 3
Step-by-step explanation:
Recall the definition of average rate of change of a function [tex]f(x)[/tex] in an interval [tex][a,b][/tex]:
Average rate of change = [tex]\frac{f(b)-f(a)}{b-a}[/tex]
In your case:
[tex]f(x) = 3x+4[/tex], and the interval [tex][a,b][/tex] i [tex][2,6][/tex], therefore:
Average rate of change = [tex]\frac{f(6)-f(2)}{6-2}=\frac{f(6)-f(2)}{4}[/tex]
Now we evaluate the function at the two requested points:
[tex]f(x)=3x+4\\f(6)=3(6)+4=18+4=22\\f(2)=3(2)+4=6+4=10[/tex], then [tex]f(6)-f(2)=22-10=12[/tex]
So finally the Average rate of change is: [tex]\frac{f(6)-f(2)}{6-2}=\frac{12}{4} =3[/tex]
