The local maximum value of the function $f(x) = {\left( {{2 \over x}} \right)^{{x^2}}}$, x > 0, is

Question

${\left( {2\sqrt e } \right)^{{1 \over e}}}$

${\left( {{4 \over {\sqrt e }}} \right)^{{e \over 4}}}$

${(e)^{{2 \over e}}}$

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