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## Homework Statement

Use the function ##f(x)=x^{1/x} \, ,\, x>0##, to determine the bigger of two numbers ##e^{\pi}## and ##\pi^e##.

## Homework Equations

## The Attempt at a Solution

I honestly don't know where to begin with this problem. I found the derivative but that seems to be of no help. The function increases when x>1/e and decreases when 0<x<1/e.

Any help is appreciated. Thanks!