CALCULUS 1000B, Winter 2023 Assignment 3 Q3. (6 marks) Solve the following optimization problems. Be sure to show your work and to justify any domains of definition 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 t hours, is given by f(t) = 13 - 912 + 24t kilometers. The first stage of the rocket has enough fuel to burn for exactly 6 hours. The rocket's second stage should be fired during this 6 hour window when the rocket's height is maximized. When should the second stage be fired? (b) A 1 m length of wire is to be cut into two pieces. The first piece will be bent to form a circle, while the second piece will be bent to form an equilateral triangle. Maximize the total area enclosed by these two shapes