Consider a particle moving along thex-axis wherex(t)

is the position of the particle at timet,x'(t)

is its velocity, andx''(t)

is its acceleration.

x(t) =t³12t²+21t5,0t10

(a) Find the velocity and acceleration of the particle.

x'(t)=x''(t)=

(b) Find the opent-intervals on which the particle is moving to the right. (Enter your answer using interval notation.)

(c) Find the velocity of the particle when the acceleration is 0.