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Proving ln(1+x)>=x - x^2/2

  1. Dec 31, 2012 #1
    1. The problem statement, all variables and given/known data
    I was asked to prove that for every x>=0, ln(1+x)>=(x-x^2/2).

    2. Relevant equations

    3. The attempt at a solution
    I defined f(x) thus: f(x) = ln(1+x) + x^2/2 - x and found f'(x)=x^2/(1+x). I hence wrote that since f'(x) is always non-negative for every x>=0 (since x^2>=0 in that domain) f(x) is likewise always positive.
    Does that suffice?
  2. jcsd
  3. Dec 31, 2012 #2


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    Science Advisor
    Homework Helper

    Pretty much. You'll want to add a comment that f(0) is non-negative as well.
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