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## Main Question or Discussion Point

Hi, I am having a little trouble understanding something my lecturer said about using the table of signs to check whether there exists a point of inflection when y'' = 0. I understand that in order for there to be a point of inflection at x

The problem I am having is that my lecturer said when checking the sign at either side of x

_{0}say, I require to check the value of y'' at either side of the value x_{0}, and if the value of y'' changes sign ( from positive to negative or vice versa ) then an inflection point exists at x_{0}.The problem I am having is that my lecturer said when checking the sign at either side of x

_{0}, you choose values a little bit smaller and a little bit larger than x_{0}. I don't understand why this is needed, I believe his explanation to be that there might be local maxima/minima that alter the value of y'' or something, but I'm not totally sure if that is what he said or why it is necessary to choose values close to x_{0}as even if that was what he said, we calculate the minima/maxima prior to working out the possible inflection points. I hope I have made myself clear and any help is appreciated.