when do we say a function is continuous
Continuous function In mathematics, a continuous function is a function for which sufficiently small changes in the input result in arbitrarily small changes in the output. Otherwise, a function is said to be a discontinuous function. A continuous function with a continuous inverse function is called a homeomorphism.
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.