Part I: Arc Length
Part II: Max Speed
(halfway between the start and end points)
If someone could help me with this problem, I would greatly appreciate the help. I believe I have the solution to the first part, but I'm not sure about the second part.
"Show that one arch of the cycloid r(t) = <t-sint, 1-cost> has length 8. Find the value of t in [0,2PI] where the speed is at a maximum"
Oops. Right you are, UCSociallyDead. Got ahead of myself.
So or , but if , you have a zero in the denominator, which doesn't work. Therefore, the only stationary point occurs at . I'll let you have the pleasure of taking another derivative to prove it's a max, not a min.