A Bound on Extreme-Value Sums

Problem

Let $f(x) = \dfrac{x^2}{2} - x\ln x - (a-1)x + a$ .

1. If $f$ has two extreme points $x_1, x_2$ , find the range of $a$ . 2. Under that condition, if $m > f(x_1) + f(x_2)$ always holds, find the range of $m$ .

Answer

Solution

Difficulty	8/10
Topics	Extrema, calculus, Monotonicity

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