A particle moving along a curve in the xy plane has position (x(t), y(t)) at time t>0, where
dx/dt = (6/t - 3)^1/3 dy/dt= te^-t
At time t=3 the particle is at the point (5,4)
a) Is there a time t at which the particle is farthest to the right? If yes, explain why and give the value of t and the x-coordinate of the position of the particle at that time. If no, explain why not. Please show your work and justify your answer