Review question

# Which is the greater of $e^{\pi}$ and $\pi^e$? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R8671

## Suggestion

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”?