A Limit to Uniform Approximation

★ 8/10functions Extrema Absolute Value inequality Casework

Problem

Let $a \in \mathbb{R}$ be such that for every real $b$ ,

\max_{x \in [0,1]} \left|x^2 + ax + b\right| \ge 1.

Find the range of $a$ .

Answer

Solution

Difficulty	8/10
Topics	functions, Extrema, Absolute Value, inequality, Casework

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