A Ratio of Parameters

★ 8/10Extrema calculus Monotonicity Logarithms inequality

Problem

Let $f(x) = \ln x + (e - a)x - 2b$ . If $f(x) \leqslant 0$ for all $x \in (0, +\infty)$ , find the minimum value of $\dfrac{b}{a}$ .

Answer

Solution

Difficulty	8/10
Topics	Extrema, calculus, Monotonicity, Logarithms, inequality

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