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

See explanation below

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

exists and is finite.

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

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Differentiability refers to the existence of the derivative of a function at a given point. A function is said to be differentiable at a point if the derivative exists at that point. Continuity, on the other hand, refers to the smoothness or uninterrupted behavior of a function over its entire domain. A function is continuous at a point if the limit of the function exists at that point and is equal to the value of the function at that point. While every differentiable function is continuous, not every continuous function is differentiable.

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