The product of minimum value of \( x^{x} \) and maximum value of \( \left(\frac{1}{x}\right)^{x}...

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The product of minimum value of \( x^{x} \) and maximum value of \( \left(\frac{1}{x}\right)^{x} \) is
(a) \( e \)
(b) \( e^{-1} \)
(c) 1
(d) \( e^{2} \)
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