- #1
songoku
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- TL;DR Summary
- By finding the critical points of f' (x) (point where f'(x) = 0 or f'(x) is undefined) and constructing the sign diagram for f', we can find point of relative maxima, relative minima and horizontal inflection of f
Using the same method for f", we can also find point where the concavity of f will change
If the sign on the sign diagram of f" changes from positive to negative or from negative to positive, this means the critical points of f" is non-horizontal inflection of f
But what about if the sign does not change? Let say f"(x) = 0 when ##x = a## and from sign diagram of f", the sign on the left and right of ##a## is both positive, what information can we get regarding point ##x=a## ? Is there a certain term to name that point?
Thanks
But what about if the sign does not change? Let say f"(x) = 0 when ##x = a## and from sign diagram of f", the sign on the left and right of ##a## is both positive, what information can we get regarding point ##x=a## ? Is there a certain term to name that point?
Thanks