An Integer Max for $a$

★ 6/10functions Extrema calculus Monotonicity Estimation Casework

Problem

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

1. Discuss the monotonicity of $f(x)$ . 2. If the equation $f(x) = a$ has two real solutions, find the largest possible integer value of $a$ .

Answer

Solution

Difficulty	6/10
Topics	functions, Extrema, calculus, Monotonicity, Estimation, Casework

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