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Theorem: Intermediate Value Theorem

Let \([a,b]\) be a closed real interval and let \(f:[a,b]\to\mathbb R\) be a continuous real function. Then \(f\) takes any value between \(f(a)\) and \(f(b)\), i.e. for each \(u\in [f(a),f(b)]\) there is at least one \(c\in[a,b]\) with \(f( c)=u\).

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Table of Contents

Proofs: 1

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Proofs: 1 2

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References

Bibliography

1. Forster Otto: "Analysis 1, Differential- und Integralrechnung einer Veränderlichen", Vieweg Studium, 1983