Constant function: Difference between revisions

Revision as of 17:01, 8 January 2006

Revision as of 00:03, 14 January 2006

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The first characterization of constant functions given above, is taken as the motivating and defining property for the more general notion of [[constant morphism]] in [[Category theory]].

In contexts where it is defined, the [[derivative]] of a function measures how that function varies with respect to the variation of some argument. It follows that, since a constant function does not vary, it'sits derivative(s), where defined, will be zero. Thus for example:

*If ''f'' is a [[real number|real-valued]] function of a real [[variable]], defined on some [[interval]], then ''f'' is constant if and only if the [[derivative]] of ''f'' is everywhere zero.