A projectile is fired vertically upward and has a position given by s(t) = -16t² + 128t + 192, for 0 ≤ t ≤ 9.

a. Graph the position function, for 0 ≤ t ≤ 9.

b. From the graph of the position function, identify the time at which the projectile has an instantaneous velocity of zero; call this time t = a.

c. Confirm your answer to part (b) by making a table of average velocities to approximate the instantaneous velocity at t = a.

d. For what values of t on the interval [0, 9] is the instantaneous velocity positive (the projectile moves upward)?

e. For what values of t on the interval [0, 9] is the instantaneous velocity negative (the projectile moves downward)?