The position of a small rocket that is launched vertically upward is given by 3(t) 2 5t2 + 4023 + 100, for 0 g t g 10, Where t is the measure 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 E t g 10. b) At what time is the instantaneous velocity zero? When observations begin at t = 0, a cell culture has 1200 cells and continues to grow according to the function p(t) = 12006, where p is the number of cells and t is measured in days. a) Compute p' (t). b) On the interval [0,4], when is the growth rate p'(t) the least? When is it the greatest