An Exists-Forall Chain

★ 8/10Extrema calculus Monotonicity inequality

Problem

Let $m$ be real, and set $f(x) = e^{x+1} - ma$ and $g(x) = ae^x - x$ . If there exists a real $a$ such that $f(x) \leqslant g(x)$ for all $x \in \mathbb{R}$ , find the range of possible values of $m$ .

Answer

Solution

Difficulty	8/10
Topics	Extrema, calculus, Monotonicity, inequality

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