#
OEF differentiability
--- Introduction ---

This module actually gathers 6 exercises on the differentiability
(definition and fundamental properties) of functions of one real variable.

### abs

What is the differentiability of the function f(x) = over the interval [-10,10]?

### Absolute order

Let : -> be the function defined by (x) = . What is the order of differentiability of ? **Instructions/Examples.**

- Type
`3` if is differentiable to order 3 but not to order 4. - Type
`0` if is continuous but not differentiable. - Type
`-1` if is not continuous. - Type
if is differentiable to any order.

### Continuity of derivative

Let : -> be a continuous function. If the derivative (x) exists for any point x , is the derivative function : -> always continuous?

### Continuity of derivative II

Let : -> be a continuous function. Suppose that the derivative (x) exists for any point x. If furthermore , is the derivative function : -> always continuous?

### Non-differentiable inverse

The function : -> defined by (x) = is bijective, but there is a point such that the inverse function ^{-1}(x) is not differentiable on . Find .

### Sided order

Let : -> be the function defined by (x) = | | | | si x < ; |

| si x . |

What is the order of differentiability of ?

**Instructions/Examples.**

- Type
`3` if is differentiable to order 3 but not to order 4. - Type
`0` if is continuous but not differentiable. - Type
`-1` if is not continuous. - Type
if is differentiable to any order.

**This page is not in its usual appearance because WIMS is unable to recognize your
web browser.**
Please take note that WIMS pages are interactively generated; they are not ordinary
HTML files. They must be used interactively ONLINE. It is useless
for you to gather them through a robot program.

- Description: collection of exercises on the differentiability of functions of one real variable. This is the main site of WIMS (WWW Interactive Multipurpose Server): interactive exercises, online calculators and plotters, mathematical recreation and games
- Keywords: wims, mathematics, mathematical, math, maths, interactive mathematics, interactive math, interactive maths, mathematic, online, calculator, graphing, exercise, exercice, puzzle, calculus, K-12, algebra, mathématique, interactive, interactive mathematics, interactive mathematical, interactive math, interactive maths, mathematical education, enseignement mathématique, mathematics teaching, teaching mathematics, algebra, geometry, calculus, function, curve, surface, graphing, virtual class, virtual classes, virtual classroom, virtual classrooms, interactive documents, interactive document, analysis, calculus, derivative, order, differentiability