Question

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

Answer 1

Answer:

Average rate of change= 3

Step-by-step explanation:

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

Average rate of change = $\frac{f(b)-f(a)}{b-a}$

In your case:

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

Average rate of change = $\frac{f(6)-f(2)}{6-2}=\frac{f(6)-f(2)}{4}$

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: $\frac{f(6)-f(2)}{6-2}=\frac{12}{4} =3$