## Is a constant a differentiable function?

For example, a constant function is infinitely differentiable – all of its derivatives are zero. A quadratic polynomial is infinitely differentiable – its third and higher order derivatives are all zero.

**Are manifolds differentiable?**

Differentiable manifolds are very important in physics. Special kinds of differentiable manifolds form the basis for physical theories such as classical mechanics, general relativity, and Yang–Mills theory. It is possible to develop a calculus for differentiable manifolds.

**Is constant function differentiable everywhere?**

Yes. f′ and all higher derivatives are identically equal to zero. Umberto P.

### What is a non differentiable manifold?

So by “non-differentiable” manifold I mean one for which every chart in its atlas is continuous but nowhere differentiable. Or in particularly, there exists a bijective map Φ:M→Rn such that Φ is continuous everywhere on M but differentiable nowhere(on M). So clearly such a thing can exist.

**Are cusps differentiable?**

Why are Functions with Cusps and Corners not Differentiable? A function is not differentiable if it has a cusp or sharp corner. As well as the problems with division by zero shown above, we can’t even find limits near the cusp or corner because the slope to the left of the cusp is different than the slope to the right.

**How do you know if something is differentiable?**

A function is formally considered differentiable if its derivative exists at each point in its domain, but what does this mean? It means that a function is differentiable everywhere its derivative is defined. So, as long as you can evaluate the derivative at every point on the curve, the function is differentiable.

#### Is every manifold smooth?

All manifolds that come to mind are smooth! By a manifold, I mean a Hausdorff, second countable, locally Euclidean space.

**Is Euclidean space a manifold?**

The basic example of a manifold is Euclidean space, and many of its properties carry over to manifolds. In addition, any smooth boundary of a subset of Euclidean space, like the circle or the sphere, is a manifold. Manifolds are therefore of interest in the study of geometry, topology, and analysis.

**Is constant function continuous everywhere?**

Yes, any function defined by f: R ->R as y=f(x)=k (any constant) is continuous in its domain i.e. wherever function is defined i.e. R (all real numbers).

## Is Y C continuous?

The graph of the constant function y = c is a horizontal line in the plane that passes through the point (0, c). Namely, if y′(x) = 0 for all real numbers x, then y is a constant function.

**Is a square a manifold?**

As a subset of the plane, the square is what is called a manifold with corners.

**Can there be a max at a cusp?**

This function has some nice “bumps” (relative max) but also some cusps! As you can see from the graph, there are many locations that will provide a maximum value of 1, but also many other locations where you see a cusp.

### What is differentiable manifold?

In mathematics, a differentiable manifold (also differential manifold) is a type of manifold that is locally similar enough to a linear space to allow one to do calculus.

**What is the importance of locally differential manifolds?**

A locally differential structure allows one to define the globally differentiable tangent space, differentiable functions, and differentiable tensor and vector fields. Differentiable manifolds are very important in physics.

**What is the difference between manifolds and rectifiable sets?**

A rectifiable set generalizes the idea of a piece-wise smooth or rectifiable curve to higher dimensions; however, rectifiable sets are not in general manifolds. Banach manifolds and Fréchet manifolds, in particular manifolds of mappings are infinite dimensional differentiable manifolds.

#### How to find the differential structure of a topological manifold?

Any topological manifold can be given a differential structure locally by using the homeomorphisms in its atlas and the standard differential structure on a vector space.