A Uniform Bound Past Two

★ 7/10calculus Tangent Line Trick Monotonicity inequality

Problem

If the inequality

2\mathrm{e}^{x-2} + (a - 2)x + 2 > 2a + a\ln(x - 1)

holds for all $x \in (2, +\infty)$ , find the range of possible values of the real number $a$ .

Answer

Solution

Difficulty	7/10
Topics	calculus, Tangent Line Trick, Monotonicity, inequality

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