An Inequality Splits $a$ and $b$

★ 7/10calculus Substitution Monotonicity inequality

Problem

Let $a, b$ be positive numbers and $\mathrm{e}$ the base of the natural logarithm. If

a\mathrm{e}^{a+1} + b < b\ln b,

determine the relationship between $b$ and $\mathrm{e}^{a+1}$ , with proof.

Answer

Solution

Difficulty	7/10
Topics	calculus, Substitution, Monotonicity, inequality

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