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NewtonlplaneMandelbrotsmooth. Assessments Computergraphical study of the critical point of Newton's method for family of cubic polynomials plambdalambdaN plambda plambda zmapsto lambda zlambda Nf mapsto mathit id frac f' lambdaN plambda plambdaplambdaM lambdainmathbb plambda notto text root of plambda text as toinfty lambda