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Greatest value of |a|+|b|+|c|

Source: Moldova NMO 2002 grade 9 problem nr.1

November 2, 2008
functioninequalitiestriangle inequality

Problem Statement

Consider the real numbers a≠0,b,c a\ne 0,b,c such that the function f(x) \equal{} ax^2 \plus{} bx \plus{} c satisfies ∣f(x)∣≤1 |f(x)|\le 1 for all x∈[0,1] x\in [0,1]. Find the greatest possible value of |a| \plus{} |b| \plus{} |c|.
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