The fuel efficiency, E, in litres per 100 kilometres, for a car driven at speed v, in km/h, is E(v) = 1600v v+6400* a) If the speed limit is 100 km/h, determine the legal speed that will maximize the fuel efficiency. b) Repeat part a., using a speed limit of 50 km/h. c) Determine the speed intervals, within the legal speed limit of 0 km/h to 100 km/h, in which the fuel efficiency is increasing. d) Determine the speed intervals, within the legal speed limit of 0 km/h to 100 km/h, in which the fuel efficiency is decreasing. Find constants a, b, and c such that the function f(x) = ax + bx + c will have a local extremum at (2,11) and a point of inflection at (1,5). Sketch the graph of f(x).