Smooth Function (original) (raw)

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Algebra Applied Mathematics Calculus and Analysis Discrete Mathematics Foundations of Mathematics Geometry History and Terminology Number Theory Probability and Statistics Recreational Mathematics Topology

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• Calculus and Analysis
• Calculus
• Differential Calculus
• Calculus and Analysis
• Functions

A smooth function is a function that has continuous derivatives up to some desired order over some domain. A function can therefore be said to be smooth over a restricted interval such as or . The number of continuous derivatives necessary for a function to be considered smooth depends on the problem at hand, and may vary from two to infinity. A function for which all orders of derivatives are continuous is called a C-infty-function.

See also

C-infty-Function, Continuous Function, Derivative, Function

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Cite this as:

Weisstein, Eric W. "Smooth Function." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/SmoothFunction.html

Subject classifications

• Calculus and Analysis
• Calculus
• Differential Calculus
• Calculus and Analysis
• Functions