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Stationary points are classified into four kinds:
Notice: Global (or absolute) maxima and minima are sometimes called global (or absolute) maximal (resp. minimal) extrema. While they may occur at stationary points, they are not actually an example of a stationary point. See absolute extremum[?] for more information about this.
Determining the position and nature of stationary points aids in curve sketching[?], especially for continuous functions. Solving the equation f'(x) = 0 returns the xcoordinates of all stationary points; the ycoordinates are trivially the function values at those xcoordinates.
The specific nature of a stationary point at x can in some cases be determined by examining the second derivative f''(x):
A more straightforward way of determining the nature of a stationary point is by examining the function values between the stationary points. However, this is limited in that it works only for functions that are continuous in at least a small interval surrounding the stationary point.
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