I'm having difficulty understanding this concept, and I was wondering if anyone could help me with this multi-step problem. I would greatly appreciate any help.
The position (x - coordinate) of a particle moving on the line y = 2 is given by x(t) = 2t^3 -13t^2 + 22t - 5 where t is time in seconds.
a) Describe the motion of the particle for t is greater than or equal to zero.
b) When does the particle speed up? slow down?
c) When does the particle change direction?
d) When is the particle at rest?
e) Describe the velocity and speed of the particle.
f) When is the particle at the point (5,2)?
I believe to find speed, one has to take the first derivative, and to find the change of direction one has to find the second derivative, but I am not even sure of this. Thank you so much.