if a function is continuous then it is differentiable at that point
Differentiable function If f is differentiable at a point x0, then f must also be continuous at x0. In particular, any differentiable function must be continuous at every point in its domain. The converse does not hold: a continuous function need not be differentiable. For example, a function with a bend, cusp, or vertical tangent may be continuous, but fails to be differentiable at the location of the anomaly.
Mean value theorem This theorem is used to prove statements about a function on an interval starting from local hypotheses about derivatives at points of the interval.
Limit of a function (the Dirichlet function) has no limit at any x-coordinate.
Continuous or discrete variable A continuous variable is one which can take on infinitely many, uncountable values.