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**Lord Darkin** Question: When a particle moves in a plane so that x=2cos3t and y=sin3t, then the speed on the interval 0 =< t =< $\displaystyle \frac{\pi}{2}$ is a maximum when t equals ...

A. 0

B. $\displaystyle \frac{\pi}{6}$

C. $\displaystyle \frac{\pi}{4}$

D. $\displaystyle \frac{\pi}{3}$

E. $\displaystyle \frac{\pi}{2}$

I took the derivatives of both x and y equations and put them in the speed formula. But now that I have the derivatives in the speed formula, I'm not sure what the next step is algebraically.

I have, all in the square root,

(36sin3t)^2 + (9cos3t)^2

So how do I expand that out and what are the next steps?