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

## Question

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

Hence, or otherwise, but without use of a calculator, determine which is the greater of $e^{\pi}$ and $\pi^e$.