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min of f(x) = (x-1)^4 +(x-2)^4 +...+(x-n)^4

Source: Germany 2000 p2

February 23, 2020
algebrapolynomialmininequalities

Problem Statement

For an integer n≥2n \ge 2, find all real numbers xx for which the polynomial f(x)=(x−1)4+(x−2)4+...+(x−n)4f(x) = (x-1)^4 +(x-2)^4 +...+(x-n)^4 takes its minimum value.
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