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The video tutorial discusses the Intermediate Value Theorem to prove that a function has a fixed point. If a continuous function f from 0 to 1 is considered, it will have a fixed point where f(x) equals x. This means there is a specific point, like 1/2, where applying f to it results in no change. Geometrically, this translates to the function crossing the line y=x. The tutorial promises to provide applications of this concept.