A Tangent-Line Gap

★ 7/10functions calculus Tangent Line Trick Convexity Logarithms inequality

Problem

Suppose there exists $a > 0$ such that

x\ln x + 2a \geqslant ax + b \qquad \text{for all } x \in (0, +\infty).

Find the maximum possible value of $b$ .

Answer

Solution

Difficulty	7/10
Topics	functions, calculus, Tangent Line Trick, Convexity, Logarithms, inequality

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