# When the derivative is equal to 1?

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?

• Perhaps you are looking for points of greatest curvature? Nov 16, 2018 at 18:49
• What, exactly, is your definition of "the higher derivative values near vertical asymptotes" and "the generally lower ones approaching the end behavior asymptote"? Those seem like very vague concepts to me. Nov 16, 2018 at 19:01
• For example, y=1/x, the derivative is $-1/x^2$. In the domain (-1,0) and (0,1), the absolute value of the derivative is greater than one, but past those points, the absolute value of the derivative is always less than 1. Nov 16, 2018 at 21:18