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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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| | | | | created: 2015-05-10 19:57:52 | modified: 2015-05-10 21:05:08 | by: bookofproofs | references: [581]

## 1.Proof: (related to "Intermediate Value Theorem")

(none)

### Bibliography (further reading)

[581] Forster Otto: “Analysis 1, Differential- und Integralrechnung einer Veränderlichen”, Vieweg Studium, 1983