Very nice! This illustrates the idea that at any time during the journey, the average speed up to that point constrains the possible average speeds for the whole journey.
I thought I’d point out that merely the first point (t1, d1) suffices to construct the second (green) line, since the lines both start at the same point (the origin).
Thanks! And yes, I could have left it at one point on each line since the origin counts, but thought two points might help drive the point (no pun intended!) home, lest one point appear to be a “lone solution”—two helps show that the green line is actually a maximum to a whole solution set rather than just a line created from one data point.
Very nice! This illustrates the idea that at any time during the journey, the average speed up to that point constrains the possible average speeds for the whole journey.
I thought I’d point out that merely the first point (t1, d1) suffices to construct the second (green) line, since the lines both start at the same point (the origin).
Thanks! And yes, I could have left it at one point on each line since the origin counts, but thought two points might help drive the point (no pun intended!) home, lest one point appear to be a “lone solution”—two helps show that the green line is actually a maximum to a whole solution set rather than just a line created from one data point.