Continuity and intrmediate value theorem

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Suppose that f is continuous on [a,b], f(z) < 0, and f (b) > 0. Set z = sup{x: f (t) < 0 for all t contained in [a, x]}. Prove that f (z) = 0. This is key to the proof of the intermediate value theorem. Incorporate the definition of least upper bound into your argument.

Reference no: EM13126907

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