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