A Differential Inequality

Problem

A differentiable function $f$ on $\mathbb{R}$ satisfies

(x - 314)\,f(2x) - 2x\,f'(2x) > 0 \qquad \text{for all } x.

Prove that $f(x) < 0$ for all $x \in \mathbb{R}$ .

Answer

Solution

Difficulty	8/10
Topics	calculus, Monotonicity

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