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In this video tutorial, the intermediate value theorem is used to demonstrate that a function has a fixed point. If a function f from 0 to 1 is continuous, it will have a fixed point where f(x) = x. This means there is a specific point, like 1/2, where applying f doesn't change the point. Graphically, this is represented by the function crossing the line y = x. Fixing point X naught can have practical applications.