Given that the function , discuss its continuity and differentiability at .
The function is differentiable at if belongs to the domain
of the function, and if . If ,
then the function is not
differentiable at . First, find for the function .
Now find for the function .
Thus, since , the function is differentiable at . Also, if the
function is differentiable at the point , then the function is
continuous at the same point. This means that the function is
continuous at as well.
So, the function is continuous and differentiable at .