Constant function: Difference between revisions

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== Derivative ==

The [[derivative]] of a function measures how that function varies with respect to the variation of some argument. It follows, since a constant function does not vary, its derivative will be zero. Indeed, suppose f(''x'') = ''c'' for all vector ''x'' in an Euclidean space and ''c'' constant. Then, for non-zero vector <math>mathit{h \ne 0}</math>

:<math>\left| {f(x + h) - f(x) \over h} \right| = \left| {c - c \over h} \right| = 0</math>.