Looking at reciprocal functions, they have 2 “turning” points, where the higher derivative values near vertical asymptotes turn into the generally lower ones approaching the end behavior asymptote, for example, taking $$y=\frac1x$$ the points are $(1,1)$ and $(-1,-1)$. It appears that these points are where the derivative is equal to $1$ or $-1$.
Looking at exponential and logarithmic functions, they also have these points where the value of the derivatives begin to sharply decrease or increase.
I’m wondering whether these points have a specific name?