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**Unformatted text preview: **approximating a zero of a function. Theorem (Mean Value). Suppose that f :[ a , b ] ! R is a differentiable function. Then there is a a < c < b such that ! f ( c ) = f ( b ) " f ( a ) b " a . One application of the Mean Value Theorem is to show that the Newton Method converges if the beginning value is close enough to the root....

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