Hi
You mean I suppose ?
Use
Question: When a particle moves in a plane so that x=2cos3t and y=sin3t, then the speed on the interval 0 =< t =< is a maximum when t equals ...
A. 0
B.
C.
D.
E.
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?
I'm still a little shaky on this. My teacher, on the answer key he gave me, gave me this all under the square root:
Then he wrote:
Simplifies to:
I'm not sure how to get to the part starting with 72 sin 3 etc. I think I understand the concept of this problem, I just want to know the algebra on the answer key.
Also, answer is pi/6
is maximum when is maximum which means when the derivative of is equal to 0
Derivative of
The derivative of is
The derivative of is
Therefore the derivative of is
In the same way the derivative of is
Therefore the derivative of is
Using the derivative of is which is equal to 0 when