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Maximum of x^(1/x)

MediumCalculus~5m

For x>0x>0, the function f(x)=x1/xf(x)=x^{1/x} has a single maximum. At what value of xx does it occur? (to 2 decimals)

Show hints (2)+
  1. Maximize ln⁡f\ln f instead of ff.
  2. Set the derivative of (ln⁡x)/x(\ln x)/x to zero.

Answer

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2.71828 (± 0.02)

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Asked at: Citadel, SIG

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