## anonymous 4 years ago Find the average rate of change of f from 0 to (11pi)/12. f(x)=tan(2x)

1. myininaya

$\frac{f(0)-f(\frac{11 \pi}{12})}{0-\frac{11 \pi}{12}}$ it would have been nice if you didn't repost this twice so i wouldn't have to type that again

2. anonymous

last time i did not include f(x)=tan(2x)

3. myininaya

$\frac{\tan(2 \cdot 0)-\tan(2 \cdot \frac{11 \pi}{12})}{-\frac{11 \pi}{12}}$ $\frac{0-\tan(\frac{11 \pi}{6})}{\frac{-11 \pi}{12}}$ it is the same thing though i mean it is the same formula to use

4. myininaya

$\frac{ \tan(\frac{11 \pi}{6})}{\frac{11 \pi}{12}} \cdot \frac{12}{12}=\frac{ 12 \tan(\frac{11 \pi}{6})}{11 \pi}$

5. anonymous

((-11pi)sqrt3)/36

6. myininaya

$\frac{12 \tan(\frac{6 \pi}{6}+\frac{5 \pi}{6})}{11 \pi}$ $\frac{12 \tan( \frac{5\pi}{6}+\pi)}{11 \pi}$

7. myininaya

|dw:1327879891939:dw|

8. myininaya

|dw:1327879937416:dw|

9. myininaya

$\frac{12 (\frac{-1}{\sqrt{3}})}{11 \pi}$

10. myininaya

does that help? do you understand?

11. myininaya

$\frac{12 (\frac{-1}{\sqrt{3}})}{11 \pi} \cdot \frac{\sqrt{3}}{\sqrt{3}}=\frac{12 (-1)}{11 \pi \sqrt{3}}$

12. myininaya

$\frac{-12}{11 \pi \sqrt{3}} \cdot \frac{\sqrt{3}}{\sqrt{3}}=\frac{-12 \sqrt{3}}{11 \pi (3)}$

13. myininaya

$\frac{-12 \sqrt{3}}{33 \pi}$

14. myininaya

$\frac{-4 \sqrt{3}}{11 \pi}$

15. anonymous

ok i need to look over everything you have been laying out for me very slowly

16. anonymous

thank you for taking the time to write this out