# How do inflection points differ from critical points?

Critical points occur when the slope is equal to $0$; that is whenever the first derivative of the function is zero. A critical point may or may not be a (local) minimum or maximum.
It is not necessary for the slope to be $0$ for a point of inflection to occur (it may or may not).
The second derivative must be $0$ for a point of inflection, but that is not by itself sufficient; the rate of change of the slope must change between positive and negative.