A Fraction Under a Parabola

Problem

Let $a, b > 0$ with $a^2 - b + 4 \leqslant 0$ , and set

u = \frac{2a + 3b}{a + b}.

Determine, with proof, whether $u$ attains a maximum and/or a minimum, and find any such extreme values.

Answer

Solution

Difficulty	7/10
Topics	Extrema, algebra, AM-GM, inequality

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