Constant function: Difference between revisions

Revision as of 17:30, 14 April 2005

Revision as of 06:52, 18 April 2005

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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's 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.

For functions between [[preorder|preordered sets]], constant functions are both [[order-preserving]] and [[order-reversing]]; conversely, if ''f'' is both order-preserving and order-reversing, and if the [[___domain]] of ''f'' is a [[lattice (order)|lattice]], then ''f'' must be constant.

Other properties of constant functions include: