## anonymous 4 years ago Find the average rate of change of f from 0 to 7pi/12. f(x)=tan(2x)

1. anonymous

(4sqrt3)/(7pi)

2. anonymous

Correct?

3. myininaya

$\frac{\tan(2 \cdot \frac{ 7 \pi}{12})-\tan(2 \cdot 0)}{\frac{7 \pi }{12}-0}$

4. myininaya

let me find out by simplifying this

5. anonymous

yes it is correct, since it starts at (0,0)

6. myininaya

$\frac{\tan(\frac{7 \pi}{6})}{\frac{7 \pi}{12}}$

7. myininaya

$\frac{12}{7 \pi} \cdot \tan(\frac{ 7 \pi}{6} )$

8. anonymous

oops i was wrong $\tan(\frac{7\pi}{6})=\frac{1}{\sqrt{3}}$

9. myininaya

$\frac{12}{7 \pi} \cdot \frac{\sin(\frac{7 \pi}{6})}{\cos(\frac{7 \pi}{6})}$ $\frac{12}{7 \pi} \cdot \frac{\sin( \pi +\frac{\pi}{6})}{\cos( \pi +\frac{\pi}{6})}$ $\frac{12}{ 7 \pi} \cdot \frac{\frac{-1}{2}}{\frac{-\sqrt{3}}{2}}=\frac{12}{7 \pi} \cdot \frac{1}{\sqrt{3}}$ lol sorry i was having a find an error in my latex

10. anonymous

No worries