A Nonnegative Range Tradeoff

★ 7/10functions AM-GM inequality Discriminant

Problem

The quadratic $f(x) = ax^2 - 4x + c$ (for $x \in \mathbb{R}$ ) has range $[0, +\infty)$ . Find the maximum value of

\frac{1}{c+1} + \frac{9}{a+9}.

Answer

Solution

Difficulty	7/10
Topics	functions, AM-GM, inequality, Discriminant

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