Smooth Function -- From Wolfram MathWorld

Home » What Is A Smooth Function » Smooth Function -- From Wolfram MathWorld

Maybe your like

Search Algebra Applied Mathematics Calculus and Analysis Discrete Mathematics Foundations of Mathematics Geometry History and Terminology Number Theory Probability and Statistics Recreational Mathematics Topology Alphabetical Index New in MathWorld
  • Calculus and Analysis
  • Calculus
  • Differential Calculus
  • Calculus and Analysis
  • Functions
Smooth Function

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 (a,b) or [a,b]. 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

Explore with Wolfram|Alpha

WolframAlpha

More things to try:

  • .999... = 1
  • deltahedra
  • graph sin t + cos (sqrt(3)t)

Cite this as:

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

Subject classifications

  • Calculus and Analysis
  • Calculus
  • Differential Calculus
  • Calculus and Analysis
  • Functions
Created, developed and nurtured by Eric Weisstein at Wolfram Research

Tag » What Is A Smooth Function