question about an inequality in calculus

Question

Please, carefully show that

$$ e^{\pi} > \pi^e $$

You are not allowed to use a calculator!

thanks

score 0 · Answer 1 · edited Dec 15 '13 at 15:07

0

Consider the function $f(x)=x/\ln(x)$. For $x \geq e$, this is an increasing function on the domain by taking its derivative. Since $\pi > e$, $f(\pi) > f(e) $and this gives the inequality.

edited Dec 15 '13 at 15:07

answered Dec 15 '13 at 14:01

Peida Tian

121

I've rewritten your math formulas using Tex. In the future, please do this yourself. – Dec 15 '13 at 14:23

question about an inequality in calculus

1 Answers1