#
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.

Other exercises on:
differentiability
continuity
calculus

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Description: collection of exercises on the differentiability of functions of one real variable. interactive exercises, online calculators and plotters, mathematical recreation and games

Keywords: interactive mathematics, interactive math, server side interactivity, analysis, calculus, derivative, order, differentiability