I am trying to find the optimum point on a curve. More specifically the function of the curve I am looking at is:
$f(x)=e^{0.3*ln(x+1)}$
and the curve looks like this:
As I read in an old stackoverflow post (https://stackoverflow.com/questions/2018178/finding-the-best-trade-off-point-on-a-curve) the way would be create a straight line connecting the first and last points of the curve and pick the point of the curve that is furthest away from the straight line.
Is the way described above a valid one for this case?
If yes what is the mathematical explanation behind it and more importantly why should it be that specific point (what does the fact that it is the furthest point away from the straight line imply?).
If not what would be the way to go?