A Guaranteed Large Value

★ 8/10functions Extrema Absolute Value inequality

Problem

Let $g(x) = |x^2 - ax - a|$ . Suppose that for every real $a$ there exists $x_0 \in [0, 1]$ with $g(x_0) \geqslant k$ . Find the range of possible values of $k$ .

Answer

Solution

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

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