Question

.Calculate the average rate of change of f(x) = 3x + 4 on the interval [2, 6]. Select any oth

Answer 1

Average rate of change= 3

Explanation:

Recall the definition of average rate of change of a function
`f(x)` in an interval
`[a,b]`:

Average rate of change =
`(f(b)-f(a))/(b-a)`

In your case:

`f(x) = 3x+4`, and the interval
`[a,b]` i
`[2,6]`, therefore:

Average rate of change =
`(f(6)-f(2))/(6-2)=(f(6)-f(2))/(4)`

Now we evaluate the function at the two requested points:

`f(x)=3x+4\\f(6)=3(6)+4=18+4=22\\f(2)=3(2)+4=6+4=10`, then
`f(6)-f(2)=22-10=12`

So finally the Average rate of change is:
`(f(6)-f(2))/(6-2)=(12)/(4) =3`