- #1

- 2,264

- 312

- 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