Sign - Part D Find the derivative of the following functions using following functions using first principles definition of derivatives, f(x) = 5x3. Show all your steps. 1. A rocket is fired into the air with an initial velocity of 98 m/s. The height ( h ) of the rocket after t seconds is given by the expression h = 98t - 4.912. a. What the average rate of change over the first 2 seconds. b. At what point does the rocket reach its maximum height? Show a graphical and algebraic solution. c. Over what intervals is the rocket's height increasing and decreasing? Part E The displacements of two ships, A and B, one hour after leaving from the same port can be represented with position vectors ?'1 = (20, 50, 0) and ! !/ = (-60, -10, 0) . Assume that the port is located at the origin and that all units are in kilometres. a. How far from the port is each ship? b. The displacement of a bird from the port can be described with the vector OC (- 65, -8, 0.5) How high above the water is the bird? How far from ship B is the bird? c. What will be the position vector of the displacement of ship A from the port 3.5 hours after leaving the port? Assume that the direction and speed of the ship are constant throughout the entire trip