Chebyshev Coefficient Sum

★ 9/10Absolute Value algebra Polynomials Estimation inequality

Problem

Let $f(x) = ax^3 + bx^2 + cx + d$ with $a \neq 0$ , and suppose $|f(x)| \leqslant 1$ for all $x \in [-1, 1]$ . Find the maximum possible value of

|a| + |b| + |c| + |d|.

Answer

Solution

Difficulty	9/10
Topics	Absolute Value, algebra, Polynomials, Estimation, inequality

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