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    NationalHardCalculus10–12

    What is the maximum value of f(x) = x e^{-x} on \mathbb{R}?

    Qual é o valor máximo de f(x) = x e^{-x} em \mathbb{R}?

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    Solution

    Step 1 of 3

    1. 1.By the product rule, f'(x) = e^{-x} - x e^{-x} = (1 - x)e^{-x}.