It's application to determining whether there is a solution in an interval is to test it's upper and lower bound. The Intermediate Value Theorem is used to prove exp (x)=2 cos (x) has at least one positive solution. Therfore: | f ( c) | 1 2 | f ( c) |. Proof. 1 Answer Sorted by: 1 We have that the mapping: h ( x) := { g ( x): x a f ( a): x = a is continuous on [ a, b]. Thus we can apply the IVT to h; I presume you can take it from there. Presented by Norman It is the By the intermediate value theorem, there is a solution of f(x) = 2 in the interval (0,1), (real) zeros. A function is termed continuous when its graph is an unbroken curve. I was playing with my iPhones level app and measuring the angle of some countertops. In this section we discuss an important theorem related to continuous functions. 1. We know that is continuous over the entire interval because it is a polynomial function. 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