Does a point of inflection of a function exist when it lies on the end of a closed interval?

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I have a function which is bounded by a closed interval. I have worked out a point of inflection, however, it lies on one of the bounds of the interval. Does the inflection point exist?

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Since the function is restricted to the closed interval, there is no other side, so it's not an inflection point.

An inflection point is a point where the concavity changes, but if there's no other side, how could it change?