In mathematics, what is the maximum value attained by the function $f (x) = x e^{- x}$ on the interval $[0, \infty)$ ?

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In mathematics, what is the nature of the roots of the quadratic equation $2 x^{2} - 4 x + 5 = 0$ ?
In mathematics, what is the derivative of the rational function $f (x) = \frac{2 x - 3}{x ^{2} + 1}$ evaluated at $x = 1$ ?
In mathematics, what is the exact value of the expression $lo g_{2} (32) - lo g_{3} (81) + ln (e^{5})$ ?
In mathematics, what is the exact value of the definite integral $\int_{0}^{1} x e^{x^{2}} d x$ ?
In mathematics, if the 3rd term of an arithmetic progression is 11 and the 7th term is 27, what is the 10th term?
In mathematics, at what value of $x$ does the cubic function $f (x) = x^{3} - 6 x^{2} + 9 x - 2$ have its point of inflection?