Which is greater e^pi or pi^e?

[Poly]

Which is greater, $e^{\pi}$ or $\pi^{e}$?

I found this when searching for calculus inequalities.

 

[Fernando Revilla]

I found this when searching for calculus inequalities.

Have a look here:

Math Forum - Ask Dr. Math

 

[Evgeny.Makarov]

A variation of the same method is to raise both numbers to power $1/(e\pi)$ and find the maximum of $x^{1/x}$.