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An inequality

  1. Dec 14, 2008 #1
    Prove/disprove the following:
    For [itex]x \geq 0[/itex], [itex] (1+x)^{1+x} \geq 1+x+x^2 [/itex].
  2. jcsd
  3. Dec 15, 2008 #2
    Well, first of all, do you think it's true?

    Second, compare derivatives.
  4. Dec 15, 2008 #3
    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 [itex](x+1)^{x+1}[/itex]. I was curious if someone could come out with a better proof.
  5. Dec 15, 2008 #4
    Well, I think that's the best way to prove the inequality then.
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