Dominating the Absolute Value

★ 8/10Monotonicity Polynomials inequality Casework

Problem

Let $f(x)=x^3+ax^2-x+1-a$ . Suppose that

|f(x)|\geqslant |x|\quad\text{for all }x\in[-1,1].

Find the range of the real number $a$ .

Answer

Solution

Difficulty	8/10
Topics	Monotonicity, Polynomials, inequality, Casework

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