Points on the graph of a function at which the derivative is zero or does not exist at all are called critical points i.e. The point (x, f (x) ) is a critical point of f (x) , if x is in the domain of 'f'' and either f ' (x) = 0 or DNE. Geometrically speaking, the tangent at such a point to the curve representing the function y = f (x) is either horizontal, vertical or DNE.