# What does it mean if a function is smooth?

## What does it mean if a function is smooth?

In mathematical analysis, the smoothness of a function is a property measured by the number of continuous derivatives it has over some domain. At the very minimum, a function could be considered smooth if it is differentiable everywhere (hence continuous).

## How do you know if a function is smooth?

Prove f(x)=1x is smooth (infinitely differentiable). The only function that comes to mind which is smooth is g(x)=ex, because it is defined on all of R, continuous everywhere, and once you prove that g′(x)=ex, you are done in showing that it is infinitely differentiable, i.e., smooth.

## What does smooth mean calculus?

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. .

## What does it mean when a graph is smooth?

A function is smooth means that the derivative exists at all points in the domain of the function and that the derivative is continuous. Geometrically, it means that the graph does not have any sharp turns and does not have a vertical tangent at any point.

## What is not smooth?

: not smooth : rough, harsh strokes his unsmooth face awkward and unsmooth writing. unsmooth. transitive verb. \ ” \

## What’s another word for not smooth?

uneven
Frequently Asked Questions About uneven Some common synonyms of uneven are harsh, rough, rugged, and scabrous. While all these words mean “not smooth or even,” uneven implies a lack of uniformity in height, breadth, or quality.

## How do you know if a curve is smooth?

A curve defined by x=f(t),y=g(t) is smooth if f′(x) and g′(x) are continuous and not simultaneously zero.

## What is a non smooth function?

Non-smooth functions include non-differentiable and discontinuous functions. functions with first derivatives with undefined regions are called non-differentiable. Graphs of non-differentiable functions may have abrupt bends.

## How do you define smooth curve?

A smooth curve is a curve which is a smooth function, where the word “curve” is interpreted in the analytic geometry context. In particular, a smooth curve is a continuous map from a one-dimensional space to an. -dimensional space which on its domain has continuous derivatives up to a desired order.

## What is another word for smooth transition?

segue
A segue is a smooth transition.

## Which is not smooth surface?

Complete answer: As we know that the surface of tyres is rough and uneven so we can say that the surface of a tyre is not a smooth surface.

## Can a smooth manifold be a differentiable manifold?

Informally, what this means is that in dealing with a smooth manifold, one can work with a single differentiable atlas, consisting of only a few charts, with the implicit understanding that many other charts and differentiable atlases are equally legitimate.

## What is the definition of a smooth function?

A smooth function is just like the name sounds: it’s a function that travels without any drop offs, jumps or other strange behavior that would make it not differentiable. More specifically, the function is differentiable up to some desired point.