Counting Solutions with a Parameter

★ 6/10functions calculus Monotonicity Casework Discriminant

Problem

Let $f(x) = \dfrac{\ln x + m}{x^2}$ .

1. When $m = 1$ , find the maximum value of $f(x)$ . 2. Determine the number of real solutions of the equation $f(x) = m - \ln x$ , discussing all cases for $m$ .

Answer

Solution

Difficulty	6/10
Topics	functions, calculus, Monotonicity, Casework, Discriminant

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