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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]

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