An Extreme Value Gap

Problem

Let

f(x) = x - \frac{1}{x} - a\ln x, \qquad a \in \mathbb{R}.

1. Find the intervals of monotonicity of $f(x)$ . 2. For $a \in \left[\dfrac{5}{2}, \dfrac{17}{4}\right]$ , let $M$ and $N$ be the local maximum and local minimum values of $f(x)$ . Find the range of possible values of $M - N$ .

Answer

Solution

Difficulty	8/10
Topics	Extrema, calculus, Monotonicity

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