Question: Let I := [a; b], let f : I R be continuous on I, and assume that f(a) < 0; f(b) > 0. Let

Let I := [a; b], let f : I → R be continuous on I, and assume that f(a) < 0; f(b) > 0. Let W := {x ∈ I : f(x) < 0}, and let w := sup W. Prove that f(w) = 0. (This provides an alternative proof of Theorem 5.3.5.)

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