# An inequality

1. Dec 14, 2008

### acarchau

Prove/disprove the following:
For $x \geq 0$, $(1+x)^{1+x} \geq 1+x+x^2$.

2. Dec 15, 2008

Well, first of all, do you think it's true?

Second, compare derivatives.

3. Dec 15, 2008

### acarchau

I have a proof which uses the first two derivatives, btw the polynomial consists of the first few three terms of the taylor expansion of $(x+1)^{x+1}$. I was curious if someone could come out with a better proof.

4. Dec 15, 2008