First derivative test
The intervals between points must be considered to know if the points are local maximas, minimas, or neither. To do this, a value from each interval is put into the first derivative of the function. If the value is positive, then it is an interval of increase. If the value is negative, then it is an interval of decrease. If two neighboring intervals change signs, that point is either a local maxima or minima. If the first interval is positive and the second interval negative, the critical point is a local maxima. If the first interval is negative and the second interval positive, the critical point is a local minima. If both intervals are positive or both intervals are negative, the critical point is not a local maxima or minima.