The functions are and .

Consider .

Find .

.

Hence .

Hence the function is continuous at any point.

Limit definition of derivatives : .

is undefined.

Hence the function is not differentiable at .

Consider .

Find .

.

Hence .

Hence the function is continuous at any point.

Limit definition of derivatives : .

.

Hence the function is differentiable at .

The function is continuous but not differentiable at .

The function is continuous and differentiable at .

.