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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?

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# Homework Help: Proving ln(1+x)>=x - x^2/2

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