Constant function: Difference between revisions

Revision as of 08:49, 13 August 2019

Revision as of 08:51, 13 August 2019

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A constant function is an [[Even and odd functions|even function]], i.e. the graph of a constant function is symmetric with respect to the ''y''-axis.

In the context where it is defined, the [[derivative]] of a function is a measure of the rate of change of function values with respect to change in input values. Because a constant function does not change, its derivative is 0.<ref>{{cite web|url=http://tutorial.math.lamar.edu/Classes/CalcI/DerivativeProofs.aspx|title=Derivative Proofs|year=2007|last1=Dawkins|first1=Paul|publisher= Lamar University|accessdate=January 12, 2014}}</ref> This is often written: &nbsp;<math>(x\mapsto c)'=0</math>&nbsp;. The converse is also true. Namely, if ''y''&#39;(''x'')=0 for all real numbers ''x'', then ''y''(''x'') is a constant function.<ref>{{cite web|url=http://www.proofwiki.org/wiki/Zero_Derivative_implies_Constant_Function|title=Zero Derivative implies Constant Function|accessdate=January 12, 2014}}</ref>

:'''Example:''' Given the constant function &nbsp; <math>y(x)=-\sqrt{2}</math> &nbsp;. The derivative of ''y'' is the identically zero function &nbsp; <math>y'(x)=(x\mapsto-\sqrt{2})'=0</math> &nbsp;.