A Monotone Cubic's Ratio

★ 7/10functions calculus Substitution AM-GM inequality Discriminant

Problem

The cubic $f(x) = ax^3 + bx^2 + cx + d$ (with $a < b$ ) is increasing on all of $\mathbb{R}$ . Find the minimum value of

\frac{a + b + c}{b - a}.

Answer

Solution

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

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