$x\ln x$ Under an Exponential

★ 7/10functions Extrema calculus Monotonicity Logarithms inequality

Problem

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

1. Find the extrema of $g(x) = \dfrac{f(x)}{x^2} - \dfrac1x$ . 2. Prove that

f(x) + 1 < \mathrm{e}^x - x^2 \qquad (x > 0).

Answer

Solution

Difficulty	7/10
Topics	functions, Extrema, calculus, Monotonicity, Logarithms, inequality

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