To obtain the value of a polynomial of degree n, whose coefficients are a0,a1,...,an (starting with the term of highest degree), when the variable x is given the value b, 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=b.
https://cdn.artofproblemsolving.com/attachments/a/a/27563a0e97e74553a270fcd743f22176aed83b.png algebrapolynomialanalysisderivative