- #1
PFuser1232
- 479
- 20
According to this link: http://tutorial.math.lamar.edu/Classes/CalcI/ShapeofGraphPtII.aspx
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.
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.