Differentiability

A function is differentiable at iff:

is called the derivative of at .

One-side differentiable

Left differentiable

A function is left-differentiable at iff:

Right differentiable

A function is right-differentiable at iff:

Differentiability implies continuity

Proof Hint

Use .

Note

Suppose is differentiable at . Define :

is continuous at .