Three Equal Values

★ 8/10functions Extrema calculus Monotonicity Logarithms

Problem

Let $f(x) = \dfrac{1 + \ln x}{x - 1}$ and $g(x) = \dfrac{k}{x}$ with $k \in \mathbb{N}^*$ . Suppose that for every $c > 1$ there exist $a, b$ with $0 < a < b < c$ such that

f(c) = f(a) = g(b).

Find the maximum value of $k$ .

Answer

Solution

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

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