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Maximum value of $f (x) = {(\frac{1}{x})}^{x}$

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$e$

$e^{1 / e}$

${(\frac{1}{e})}^{e}$

$e^{e}$

answer is A.

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Detailed Solution

$f^{1} (x) = 0 \Rightarrow x = 1 / e$
$f^{1} (x)$ changes its sign from +ve to –ve
$∴$ maximum value $f (1 / e)$

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