Smooth function

In mathematics, a smooth function is one that is infinitely differentiable, i.e., has derivatives of all finite orders. A function is called C if it is a continuous function. A function is C1 if it has a derivative that is continuous; such functions are also called continuously differentiable. A function is called Cn for n ≥ 1 if it can be differentiated n times, with a continuous n-th derivative. The smooth functions are therefore those that lie in the class Cn for all n. They are also called C∞ functions.

Related Topics:
Mathematics - Derivative - Continuous function

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

For example, the exponential function is evidently smooth because the derivative of the exponential function is the exponential function itself.

~ ~ ~ ~ ~ ~ ~ ~ ~ ~