[tasdrouille]

Building on Robert's idea, of letting it start backwards with the clutch disengaged. You now have two scenarios. 1- The car reachs a speed at the bottom of the wave at which the engine would rev past its efficiency island. 2- The car never makes it to the most efficient speed just rocking back and forth from it's innitial potential energy.

Scenario 1: You let it rock backwards up the left hand side of the wave. From there going down it will cross the most efficient rpm somewhere before the bottom of the wave. It will also cross it back while slowing down somewhere on its way back up the wave to the car's original starting point. Assuming your new "starting position" is now on the left hand side of the wave pointing down, you then calculate and subsequently execute two pulses, both as close to the efficiency island load and rpm as they can be, one on the way down and one on the way up, that will give you the energy needed to get over the first wave.

Scenario 2: You let it rock backwards so your new starting position is on the left hand side of the wave pointing down and you do one single pulse starting at the very bottom of the wave, where you're speed will be the greatest.

Edit: Thinking about it, for scenario 1 the car should be rocking back and forth in the starting wave while applying infinitesimal bursts each time the sweet spot speed is crossed when the car is going forward, the amplitude of the movement increasing all the way untill the car can go over the first wave.

I have long been suspecting the definitive answer is lying in an unpractical particularity of the excercise, mostly irrelevant to the real world.