A Product Below $m\mathrm{e}^2$

★ 7/10functions Extrema calculus Substitution Monotonicity inequality

Problem

The function $f(x) = \ln x + \dfrac{m}{x} - 3$ has two zeros.

1. Find the range of possible values of $m$ . 2. Let $a, b$ be the two zeros of $f(x)$ . Prove that

ab < m\mathrm{e}^2.

Answer

Solution

Difficulty	7/10
Topics	functions, Extrema, calculus, Substitution, Monotonicity, inequality

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