Which of the following is true?
- $\log(1+x) < x- \frac{x^2}{2} + \frac{x^3}{3} \text{ for all } x>0$
- $\log(1+x) > x- \frac{x^2}{2} + \frac{x^3}{3} \text{ for all } x>0$
- $\log(1+x) > x- \frac{x^2}{2} + \frac{x^3}{3} \text{ for some } x>0$
- $\log(1+x) < x- \frac{x^2}{2} + \frac{x^3}{3} \text{ for some } x>0$
