# What is the difference between differentiability and continuity of a function?

##### 1 Answer

See explanation below

#### Explanation:

A function

exists and is finite and equals the value of the function:

A function

exists and is finite.

A differentiable function is always continuous.

We can prove it by writing

Passing to the limit for

A function can be continuous but not differentiable, for example:

is continuous but not differentiable in