According to this link: http://tutorial.math.lamar.edu/Classes/CalcI/ShapeofGraphPtII.aspx(adsbygoogle = window.adsbygoogle || []).push({});

The second derivative test can only be applied if ##f''## is continuous in a region around ##c##.

But according to this link: http://calculus.subwiki.org/wiki/Second_derivative_test#Requirement_of_twice_differentiability

##f''## need not be defined in a region around ##c##.

I'm confused as to what is required for the second derivative test.

##f''## is allowed to have a discontinuity at ##c##, but not around ##c##? If ##f''## is continuous around ##c##, then ##\lim_{x→a} f''(x)## must equal ##f''(a)## where ##a## is in some region around ##c##, but according to the second link, ##f''(a)## doesn't have to be defined.

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# Second derivative test

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