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MeanIntermediateValue

# MeanIntermediateValue - approximating a zero of a function...

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The Intermediate Value Theorem and the Mean Value Theorem We give the correct statements of the Intermediate Value Theorem and the Mean Value Theorem . Theorem (Intermediate Value). Suppose that f :[ a , b ] ! R is a continuous function. Suppose that d is between the values f ( a ) and f ( b ) . Then there is a a < c < b such that f ( c ) = d . One application of the Intermediate Value Theorem is the Bisection Method for
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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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