3. (5 pts each) A particle moves along the x-axis. Its position on the x-axis at time t seconds is given by the function r(t) = t4 - 4t³ - 2t2 + 12t. Consider the interval -4≤ t ≤ 4. Grouping terms may help with factoring.
(a) When is the particle moving in the positive direction on the given interval?
(b) When is the particle moving in the negative direction on the given interval?
(c) What is the particles average velocity on the given interval?
(d) What is the particles average speed on the interval [-1,3]?