This theorem is a consequence of both the boundedness theorem and the fact that the reciprocal of the difference of a function minus its least upper bound on a compact set cannot be bounded.
This theorem is a consequence of both the boundedness theorem and the fact that the reciprocal of the difference of a function minus its least upper bound on a compact set cannot be bounded. Though it is not a more general case of Rolle's theorem, it can be used to prove Rolle's theorem, and the points predicted to exist by this theorem and Rolle's theorem turn out to be identical. In some proofs of the fundamental theorem of calculus, this is applied before the intermediate value theorem. Name this theorem which states that any continuous function over a bounded and closed interval must attain minimum and maximum values.
This theorem is a consequence of both the boundedness theorem and the fact that the reciprocal of the difference of a function minus its least upper bound on a compact set cannot be bounded.
{extreme value theorem} [or {EVT}]