Calculus - Curve Sketching

Question

A point on a graph where the second derivative is zero

1. is an inflection point
2. may be an inflection point
3. is a local minimum
4. is a local maximum

Answer 1

Consider y = x^3 and y = x^4.

For both, y'' = 0 at 0

However,

For y = x^3, there is an inflection at 0, while for y = x^4, there is a minimum