The following question was presented to me by a tutoring student in AP Calculus. It's supposedly from a practice test - not sure if it's official. Here's the issue.
Below I've reproduced the complete graph of some continuous function $f(x)$. The question asks us to identify what $x$ are inflection points and to offer an explanation as to why. My student's teacher provided her class with an answer that $x=2$ is an inflection point. I disagree.
$f'(x)$ is discontinuous at $x=2$ and $f''(x)$ does not exist! Furthermore, there is no tangent at $x=2$. I see no transition from concavity to convexity anywhere here. From the definitions of an inflection point provided in Stewart's and Thomas's textbooks, no inflection points exist. Can anyone chime in here? Is anyone aware of an alternate definition of inflection point - especially one that is taught in US high schools - that could have been intended here?