The position of a small rocket that is launched vertically upward is given by s(t) = -5t² + 40t + 100, for 0 ≤ t ≤ 10, where t is measured in seconds and s is measured in meters above the ground.

a. Find the rate of change in the position (instantaneous velocity) of the rocket, for 0 ≤ t ≤ 10.

b. At what time is the instantaneous velocity zero?

c. At what time does the instantaneous velocity have the greatest magnitude, for 0 ≤ t ≤ 10?

d. Graph the position and instantaneous velocity, for 0 ≤ t ≤ 10.