Zeros Multiply Past $\mathrm{e}^2$

★ 7/10functions calculus Monotonicity Logarithms inequality

Problem

The function $f(x) = ax - \ln x$ has two zeros $x_1, x_2$ .

1. Find the range of possible values of $a$ . 2. Prove that $x_1 x_2 > \mathrm{e}^2$ .

Answer

Solution

Difficulty	7/10
Topics	functions, calculus, Monotonicity, Logarithms, inequality

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