When the Equation Has a Solution

★ 5/10functions Extrema calculus Monotonicity

Problem

Let $f(x) = \dfrac{1}{x} + k\ln x$ with $k \neq 0$ .

1. When $k = 1$ , find the intervals of monotonicity and the extreme values of $f(x)$ . 2. If the equation $f(x) = k$ has a solution, find the range of possible values of the real number $k$ .

Answer

Solution

Difficulty	5/10
Topics	functions, Extrema, calculus, Monotonicity

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