Which is the greater of $e^{\pi}$ and $\pi^e$?

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Show that for \(x>0\), \(x^{1/x}\) has its greatest value when \(x=e\).

How would you differentiate an exponential function such as \(2^x\)?

Could you apply a modification of that technique here?

Could we write \(x^{1/x}\) as “\(e\) to the power something”?