The Intermediate value theorem explains how a function is continuous over a given interval. If a function is continuous over a given interval then there is a value of that function. Determining if it is continuous or not allows us to find the possible limits within the problem. The Intermediate value theorem is a existence theorem because it shows the value between two points whether it is continuous or not and whether it has to pass through a point to go to another.
Good explanation. One minor change- an existence theorem tells us that the point exists. It does not tell us what the value of teh point is.
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