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calculation of value of derivative of given polynomial with flowchart

Source: Spanish Mathematical Olympiad 1967 P8

December 4, 2022
algebrapolynomialanalysisderivative

Problem Statement

To obtain the value of a polynomial of degree nn, whose coefficients are a0,a1,...,ana_0, a_1, . . . ,a_n (starting with the term of highest degree), when the variable xx is given the value bb, the process indicated in the attached flowchart can be applied, which develops the actions required to apply Ruffini's rule. It is requested to build another flowchart analogous that allows to express the calculation of the value of the derivative of the given polynomial, also for x=bx = b. https://cdn.artofproblemsolving.com/attachments/a/a/27563a0e97e74553a270fcd743f22176aed83b.png
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