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Theorem: Intermediate Root Value Theorem (Bolzano)

Let \([a,b]\) be a closed real interval and let \(f:[a,b]\to\mathbb R\) be a continuous real function with $f(a) < 0$ and $f(b) > 0$ (or $f(a) > 0$ and $f(b) < 0$). Then there is a root value $x\in[a,b]$ with \(f(x)=0\).

| | | | | created: 2017-04-17 13:00:31 | modified: 2017-07-31 21:15:48 | by: bookofproofs | references: [581]

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

Edit or AddNotationAxiomatic Method

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Bibliography (further reading)

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