The Largest $a$ with a Dip

★ 6/10functions Extrema Completing the Square Polynomials inequality

Problem

Let $f(x) = x^3 - ax^2 + \left(a^2 - 2\right)x + 1$ . If there exists $m > 0$ with $f(m) \leqslant 0$ , find the maximum possible value of the real number $a$ .

Answer

Solution

Difficulty	6/10
Topics	functions, Extrema, Completing the Square, Polynomials, inequality

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