The problem states that a particle's position at time t is given by the equation: [tex]x(t)=2\pi t+cos(2\pi t)[/tex] Therefore, the velocity of the particle at time t would be the first derivative of the above equation: [tex]x'(t)=v(t)=2\pi-2\pi(sin(2\pi t))[/tex] I was asked what the maximum velocity of the particle was, and was able to determine that it is 2, but that is only because I used a graphing aid. I am not quite sure where to start on how to find the maximum, other than know what the graph looks like in one's mind's eye, but that seems a little too extreme. I have also calculated the second derivative (acceleration of the particle) if it is needed: [tex]x''(t)=a(t)=4\pi^2cos(2\pi t)[/tex] I would show other attempt at work, but we really weren't shown how to do this. But yes, we still have to do it. Thank you for your help.