Question: Let I := [a, b and let f : I R be a continuous function such that f(x) > 0 for each x in

Let I := [a, b and let f : I → R be a continuous function such that f(x) > 0 for each x in I. Prove that there exists a number a > 0 such that f(x) > a for all x ∈ I.

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