Q3. (6 marks) Solve the following optimization problems. Be sure to show your work and to justify any domains of denition for your functions. (a) A rover on Mars has just collected a very interesting soil sample. It will launch a two stage rocket to send the sample to an orbiting satellite for further analysis. The distance above the surface of Mars that the rocket carrying the sample is, after 15 hours, is given by t) 2 t3 9t2 + 2413 kilometers. The rst stage of the rocket has enough fuel to burn for exactly 6 hours. The rocket's second stage should be red during this 6 hour window when the rocket's height is maximized. When should the second stage be red