As long as we are picking nits, the definition of inflection point at least sometimes is written to require more than a change in concavity. It also requires that the second derivative exist at the point in question. Thus a sharp turn cannot be a point of inflection. I don't know how universal this definition is but it apeals to me. It seams "right" to me to say that a sharp turn can be a relative extrema but not an inflection point.