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The figure shows the graph of a function f Suppose that Newton s method is...

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Algebra

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The figure shows the graph of a function f Suppose that Newton s method is used to approximate the roots of the equation f x 0 with initial approximation x 6 y4 1 0 1 T a Draw the tangent lines that are used to find x and x3 and estimate the numerical values of x and X3 Round your answers to one decimal place x2 x3 b Would x 8 be a better first approximation Explain We know that x 8 Select be a better first approximation because the tangent line at x 8 intersects the x axis Select s than does the first approximation X 6

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