Velocity is equivalent to a specification of an object’s speed and direction of motion (e.g. 60 km/h to the north). How to get is, Choose a point to the left of the extremum and another point just to the right. If acceleration is negative to the left and positive to the right, the point is a minimum velocity. If acceleration is positive to the left and negative to the right, the point is a maximum velocity. There you go.
Maximum velocity is reached when you stop accelerating, because this is when you can't gain anymore speed, i.e. acceleration is zero. In other words the derivative of velocity is equal to zero. However, zero acceleration can also result in minimum velocity because you can't lose any more speed.
