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Intermediate Value Theorem

If f is continuous on [a, b] and f(a) ≠ f(b) then for any value c (f(a), f(b)), there is at least one number x0 in (a, b) for which f(x0) = c.
 
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From Figs. 3 and 4, it is clear that continuity in the interval [a, b] is essential for the validity of this theorem.




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