Hello,

The question is: use the mean value theorem to show that for all x > 0

$\displaystyle \frac{1}{\sqrt{1 + x}} - 1 > -\frac{1}{2}x$

and

$\displaystyle \ln(3 + x) - \ln(3) \leq \frac{x}{3}$

How do I do this? I thought you always need 2 x-values (a and b) and then use $\displaystyle \frac{f(b)-f(a)}{b-a}$ to find the mean slope, but this is an entire different context...

How do I do this? Thanks!