Question

How do you find the average rate of change of $F\left(x\right)=3+x^3$ from 0 to 2?

Answer 1

4

Explanation:

The average rate of change of a continuous function,

f(x), on a closed interval [a, b] is given by

$\overline{f\left(x\right)}=\frac{f\left(b\right)-f\left(a\right)}{b-a}$

So the average rate of change of the function $f\left(x\right)=3+x^3$ on [0, 2] is:

$Aroc=\frac{f\left(2\right)-f\left(0\right)}{2-0}$

$=\frac{(3+2^3)-(3+0)}{2}$

$=\frac{\left(11\right)-\left(3\right)}{2}$

$=\frac{8}{2}$

$=4$