Probably a toughie unless the data are very clean (w/o noise, scatter, etc.)
Best guess w/o any data to actually play with might be to start w/ a linear fit on the left adding points until the goodness of fit begins to degrade. Of course, if it's noisy it may be quite a ways past the first curvature point before there's enough variation to pick it out...
I'd suppose there would be literature in the field one should be able to find...