We can locate the position of stationary points by looking for points where y' =dy/dx = 0.

It is possible that some such points will not be turning points.

We can calculate second derivative i.e. y'' = d²y/dx² at each point we find.

If y'' is positive then the stationary point is a minimum turning point.

If y'' is negative then the stationary point is a maximum turning point.

If y''=0, it is possible that we have a maximum, or a minimum, or indeed other sorts of behaviour. So if y'' = 0 this second derivative test does not give us useful information and we must seek an alternative method