The function \small{s(t)} describes the position of a particle moving along a coordinate line,
where \small{s} is in feet and \small{t} is in seconds.
\small{s(t) = t^{3}-6t^{2}+9t+6, \qquad t \ge 0}

(e) Over what interval(s) does the particle have negative acceleration?
Use ** inf ** to represent \small{\infty} , and ** U ** for the union of sets.

(f) Over what interval is the particle speeding up? Slowing down?
Use ** inf ** to represent \small{\infty} , and ** U ** for the union of sets.

(a) Find the velocity and acceleration functions.

(b) Over what interval(s) is the particle moving in the positive direction?
Use ** inf ** to represent ** U ** for the union of sets.

Interval: |

(c) Over what interval(s) is the particle moving in the negative direction?
Use ** inf ** to represent ** U ** for the union of sets.

Interval: |

(d) Over what interval(s) does the particle have positive acceleration?
Use ** inf ** to represent ** U ** for the union of sets.

Interval: |

Interval: |

Speeding up: | |

Slowing down: |

You can earn partial credit on this problem.