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> In the long run, it absolutely is. It's possible for any given point on the curve to have a positive first derivative and a negative second derivative, but if
by JoshuaDavid 5y ago
> In the long run, it absolutely is. It's possible for any given point on the curve to have a positive first derivative and a negative second derivative, but if the second derivative stays negative, the first derivative will also ultimately turn negative.
f(x) = log(x) is a function where, at every positive x, the first derivative is positive and the second derivative is negative. As a growth curve, that would look like a constant amount of effort being put towards improvements, but the amount of improvement per unit of effort spent decreasing exponentially.
- philwelch 5y agoFair point, and I stand corrected. That may even be a good model for scientific progress.