A differentiable function is one that has a derivative at every point in its domain.
This means the function has a well-defined tangent line at each point, and the slope of this tangent line changes smoothly.
Continuity Differentiability
If a function is differentiable at a point, then it must be continuous at that point.
However, a function can be continuous at a point without being differentiable there.
E.g. is continuous everywhere but not differentiable at ; has a vertical tangent at , i.e. not differentiable there.