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Properties of Points of Inflection
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All of the following statements regarding points of inflection and the second derivative are true EXCEPT:

A

A point of inflection occurs when the concavity of a function changes.

B

A point where the second derivative equals zero is always a point of inflection.

C

One must test intervals around a candidate point to confirm a change in concavity for it to be an inflection point.

D

If there is no sign change in $$f''(x)$$ around a zero, then that point is not an inflection point.

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