Intermediate Value Theorem | Fixed Point Theorem | Use IVT to prove Fixed Point | Calculus - Part 5 скачать в хорошем качестве

Intermediate Value Theorem | Fixed Point Theorem | Use IVT to prove Fixed Point | Calculus - Part 5

In this video we use IVT or Intermediate Value Theorem to prove Fixed point theorem (Brouwer fixed-point theorem). In mathematics, a fixed-point theorem is a result saying that a function F will have at least one fixed point (a point x for which F(x) = x), under some conditions on F that can be stated in general terms. Some authors claim that results of this kind are amongst the most generally useful in mathematics. In mathematical analysis, the intermediate value theorem states that if f is a continuous function whose domain contains the interval [a, b], then it takes on any given value between f(a) and f(b) at some point within the interval. This has two important corollaries: If a continuous function has values of opposite sign inside an interval, then it has a root in that interval (Bolzano's theorem). The image of a continuous function over an interval is itself an interval.