If the function f ( x ) = ( 1 x ) 2 x ; x > 0 attains the maximum value at x = 1 e then [2024]

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Solution

Q.
If the function $f (x) = {(\frac{1}{x})}^{2 x}; x > 0$ attains the maximum value at $x = \frac{1}{e}$ then [2024]

1 ${(2 e)}^{π} > π^{(2 e)}$

2 $e^{2 π} < {(2 π)}^{e}$

3 $e^{π} > π^{e}$

4 $e^{π} < π^{e}$

Ans.
(3)

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