A question for all you math scholars.
If the first derivative of a function is positive the the function is increasing. But increasing is a more general description as the function need not be differentiable.
If the second derivative of a function is positive the the function is convex. But again convexity is more general.
Is there a general name for f’’’ > 0.
You could say the first derivative is convex, but that requires a first derivative. Is there a name with reliance on any derivatives?
Answering my own question if anyone else is interested. The general notion is called positive aberrancy, but apparently that term has not been taught since 1900. (And the SDMB spell checker doesn’t admit that word.)
See https://www.jstor.org/stable/2690245?seq=1#metadata_info_tab_contents
You could also say “increasing convexity” if you didn’t want to bring derivatives back into it again
In Physics, the derivatives have names because of the real-world models. But the name just identifies the derivative, and says nothing about the shape of the function. Position, velocity, acceleration, jerk, dunno if official names go any deeper.
Aberration is a term used in optics, and is sort of derivative-related (the various flaws could be represented as graphs with curvature and all that), but aberrancy just sounds weird.
Unofficially, snap, crackle, and pop
In general, you would be interested in the kurtosis of jerk, rather than its sign. I believe that the same would be true for aberrancy, but I have no intuitive understanding of the relationship between lens shape and beam shape.
I’ve seen these terms too for the higher derivatives – but they have nothing to do with whether those derivatives are positive or negative.
As long as you stick with higher derivatives of ex it’s no problem.
In my experience (which may or may not be representative) it’s more common to say that it’s “concave upward” (as opposed to “concave downward” for a negative second derivative) than “convex.”