## anonymous 4 years ago Need help in finding the rate of change

1. anonymous

s(t) = (t - pi / t + 6 pi) ^ 1/3

2. anonymous

t = 2pi

3. anonymous

srry dont really know how to use the equatio button

4. anonymous

average rate of change over what interval?

5. anonymous

it is using derivative to find it

6. anonymous

oooooooooooh ok you want the derivative evaluated at $2\pi$ right?

7. lalaly

rate of change is $\frac{ \Delta s}{\Delta t} = \frac{ds}{dt}$

8. anonymous

$s(t)=\left (\frac{t-\pi}{t+6\pi}\right) ^{\frac{1}{3}}$ yes?

9. anonymous

yess

10. anonymous

my teacher didnt use displacement over time...only derivatives

11. anonymous

ok so derivative is $\frac{1}{3}\left( \frac{t-\pi}{t+6\pi}\right)^{-\frac{2}{3}}\times \frac{7\pi}{(x+6\pi)^2}$

12. anonymous

ugly enough. replace x by $2\pi$ see what you get

13. anonymous

ahh..i dont know how to use the equations.. so it is 1/3 ( pi / 8pi ) ^ -2/3 x ( 7 pi / 8pi )^2

14. anonymous

i think i get it now thx