Smoothness

Uncommon card · No. 132944

In mathematical analysis, the smoothness describes the number of times a function can be differentiated without producing discontinuities. The smoothness, or differentiability class, is an integer k {\displaystyle k} such that a function has all derivatives up to order k {\displaystyle k} , and such that all of these derivatives are continuous. One says that such a function has class C k {\displaystyle C^{k}} . For example, the absolute value function f ( x ) = | x | {\displaystyle f(x)=|x|} has class C 0 {\displaystyle C^{0}} , because it is continuous, but not differentiable...

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