Question: Let I := [a, b] and let f : I R be a continuous function on I such that for each x in I

Let I := [a, b] and let f : I → R be a continuous function on I such that for each x in I there exists y in I such that | f (y)| < ½| f(x)|. Prove there exists a point c in I such that f(c) = 0.

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