- #1
peripatein
- 880
- 0
Hello,
I was asked to prove that for every x>=0, ln(1+x)>=(x-x^2/2).
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?
Homework Statement
I was asked to prove that for every x>=0, ln(1+x)>=(x-x^2/2).
Homework Equations
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?