Question

If the second derivative is 0, does that mean the function has a point of inflection there?

Answer 1

No.
Example: \(\Large\rm \quad y=x, \qquad\qquad y''=0\)
This function has no inflection point, yet the second derivative is zero.

Answer 2

Alternatively, if you `set` your second derivative equal to zero, and are able to find an x that corresponds to this, then yes, you have an inflection point.
Example: \(\Large\rm \quad y=x^3,\qquad\qquad y''=6x\)
Setting our second derivative equal to zero shows us that we have an inflection point at x=0.\[\Large\rm 0=6x, \qquad\qquad 0=x\]

Answer 3

An inflection point occurs when the concavity changes. If the second derivative is zero, it doesn't necessarily imply that it changed signs.

The derivative could have went from + to zero to + again. This is not an inflection point, but its 2nd derivative is zero.