Answer the following with complete solutions

1. The position function of a cyclist traveling along a line is given by as) = r\" st? +15t s where s is is miles and l' is in hours. {f3 points) {a} Is the cyclist speeding up or slowing down at time t = 4 hours? [b] Determine the total distance traveled by the cyclist in the rst ti hours. [c] Find the instantaneous rate of change of the acceleration of the cyclist with respect to time at t = 1 hour. _ 2 2 2. Find {algebraically} the absolute maximum and minimum values of r} = {II2} on the interval {[1, +430}, if any, and state where those values occur. If f has no absolute maximum or minimum value~ explain why. {5 points) 3. A town on one island is to be supplied by electricity from a power plant on another island. The islands are 3|] km apart and both are Ev' km from the {same} shore of the main island. It cost-s Php 2 million per km to lay an underwater cable and Php 1 million per km to lay cables on the shoreline. To cut costs._ the cable will run from the power plant to a point A on the shore1 then along the shore from point A to point B, then from point B on the shore to the town. If the length of the underwater cables from the power plant to point A and from point B to the town are equal~ how long should the cable be from point A to point B on the shore to minimize the cost of laying the cables? (E points)