The position of a particle moving along the x-axis is given byx(t) = t^3 + 9t^2 − 21t with t is in [0, 2]. (a) Find the velocityand acceleration of the particle.
(b) For what t-values is the velocity 0? (Enter your answers asa comma-separated list.)
(c) When is the particle moving to the left (velocity isnegative)? (Enter your answer using interval notation.)
When is the particle moving to the right (velocity is positive)?(Enter your answer using interval notation.) (
d) What is the farthest the particle gets to the left? What isthe farthest the particle gets to the right?
(e) When is the velocity increasing? (Enter your answer usinginterval notation. If an answer does not exist, enter DNE.) When isthe velocity decreasing? (Enter your answer using intervalnotation. If an answer does not exist, enter DNE.)
(f) What is the maximum velocity of the particle? v =
