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## Main Question or Discussion Point

I've been searching for some indication of the "significance" of higher order derivatives, but without much luck. Perhaps someone here can offer some insight.

The first derivative of a function f(x) (with respect to x) gives the slope of the tangent to the curve of that function. When this derivative is 0, the function is at a local extremum.

The second derivative of a function gives the concavity, and when this is 0, it is a critical point of the function.

What would the analog for third derivative be, (and for higher order derivatives)?

Or is it perhaps the case that our brains are not prepared to fathom their significance?

BiP

The first derivative of a function f(x) (with respect to x) gives the slope of the tangent to the curve of that function. When this derivative is 0, the function is at a local extremum.

The second derivative of a function gives the concavity, and when this is 0, it is a critical point of the function.

What would the analog for third derivative be, (and for higher order derivatives)?

Or is it perhaps the case that our brains are not prepared to fathom their significance?

BiP