Question

Determine the average rate of change of the function f(x)=x+x^3 between x = 0 and x = 3

Answer 1

So the average rate of change will be given by:\[\Large \frac{f(3)-f(0)}{3-0}\]

Answer 2

\[\Large f(\color{royalblue}{x})\quad=\quad (\color{royalblue}{x})+(\color{royalblue}{x})^3\]
Do you understand how we find f(3) and f(0)?
Maybe the colors will help.\[\Large f(\color{royalblue}{3})\quad=\quad (\color{royalblue}{3})+(\color{royalblue}{3})^3\]\[\Large f(\color{royalblue}{0})\quad=\quad (\color{royalblue}{0})+(\color{royalblue}{0})^3\]

Answer 3

30 and 0

Answer 4

Mmm yah that sounds right :)
So what do you get when you plug all of the pieces in?

Answer 5

0 and 30 when I plugged it in

Answer 6

Ya 30 and 0 sound right :)
Plug them in like this and simplify.
\[\Large \frac{f(3)-f(0)}{3-0}\qquad=\quad \frac{30-0}{3-0}\]