Pinning a Cubic

Problem

Let f(x)=8x3+ax2+bxf(x) = 8x^3 + ax^2 + bx. Do there exist real numbers a,ba, b such that f(x)2|f(x)| \leqslant 2 for all x[1,1]x \in [-1, 1]? If so, find all such a,ba, b; if not, explain why.

Answer

Solution

Difficulty7/10
TopicsAbsolute Value, algebra, Polynomials, inequality

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