From an unknown number of points, I have two points, e.g. (0,105) and (100,108). I also know the average, e.g. 110, of all the unknown and known points.
Would it be possible to estimate a maximum value of the points, using only the two known points and the average?
The context of the problem is that I know the speed of a car at one point, and its speed at another point later on. I also know the distance between the two points and the time it took the car to drive the distance, hence its average speed. But I'm trying to estimate the car's top speed.
The problem is: I don't know the car's speed at any other point than the two known and I don't know the acceleration or deceleration of the car at any point.
Are there any mathematical ways of doing this correctly or any paper presenting the idea, either as a mathematical problem, or in the context of speed detection.
There is no such way. Consider this in real life: You observe a car and its speed in one place, then your friend, some time later, observes the car and its speed somewhere else. We have no way of telling whether it held a constant speed between the two points, or took a break right after he passed you, then drove with the speed of light over to your friend (slowing down right before he passed your friend).