A Quadratic Bound on $x\ln x$

★ 5/10functions Extrema calculus Monotonicity Logarithms

Problem

Let $f(x) = x \ln x$ .

1. Let $g(x) = \dfrac{f'(x)}{x}$ . Find the extreme points of $g(x)$ . 2. If for all $x_2 > x_1 > 0$ we have

\frac{m}{2}\left(x_2^2 - x_1^2\right) > f(x_2) - f(x_1),

find the range of possible values of the real number $m$ .

Answer

Solution

Difficulty	5/10
Topics	functions, Extrema, calculus, Monotonicity, Logarithms

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