Three Zeros of a Nested Function

★ 7/10functions calculus Substitution Monotonicity Casework

Problem

The function

f(x) = \left(2ax + \frac{\ln x}{x}\right)\ln x - (a-1)x^3

has three distinct zeros. Find the range of possible values of the real number $a$ .

Answer

Solution

Difficulty	7/10
Topics	functions, calculus, Substitution, Monotonicity, Casework

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