Can inflection points be found in critical numbers in a function's second derivative

Zeros of the second derivative are POSSIBLE inflection points. Any point at which f(x) is defined and f "(x) is either zero or undefined CAN be an inflection point and IS, if the second derivative changes sign about that point (goes from positive to negative or from negative to positive).

Yes,because the concavity changes at the values of x where f " (x) = 0

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