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Maximum and minimum value of |a| + |b| + |c|

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August 29, 2010
inequalitiestriangle inequalityinequalities proposed

Problem Statement

Establish the maximum and minimum values that the sum ∣a∣+∣b∣+∣c∣|a| + |b| + |c| can have if a,b,ca, b, c are real numbers such that the maximum value of ∣ax2+bx+c∣|ax^2 + bx + c| is 11 for −1≤x≤1.-1 \leq x \leq 1.
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