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ax^3 + bx^2 + cx inflection point

Source: Spanish Mathematical Olympiad 1966 P8

December 4, 2022
functionalgebraanalysis

Problem Statement

Determine the values of a,b,ca, b, c, so that the graphical representation of the function y=ax3+bx2+cxy = ax^3 + bx^2 + cx has an inflection point at the point of abscissa x=3 x = 3, with tangent at the point of equation xāˆ’4y+1=0.x - 4y + 1 = 0. Then draw the corresponding graph.
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