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Minimize |x^3 - ax^2 - bx - c|

Source: China TST 2001, problem 6

May 22, 2005
algebrafunctioncalculuspolynomialminimization

Problem Statement

Let F=max⁡1≤x≤3∣x3−ax2−bx−c∣F = \max_{1 \leq x \leq 3} |x^3 - ax^2 - bx - c|. When aa, bb, cc run over all the real numbers, find the smallest possible value of FF.
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