# Thread: Mean Value Theorem proof

1. ## Mean Value Theorem proof

Could someone prove this by the mean value theorem:
-ln(1-x) < x/(1-x) for 0 < x< 1

I got really close to it..

2. Use the mean value to prove Napier’s inequality: if $\displaystyle 0<a<b$ then $\displaystyle \frac{1}{b}\le\frac{\ln(b)-\ln(a)}{b-a}\le\frac{1}{a}$.
Then let $\displaystyle a=1-x~\&~b=1$.

3. why do you let a=1-x? not a=x

4. Originally Posted by Monster32432421
why do you let a=1-x? not a=x
Because $\displaystyle a=1-x$ gives us what we want.
But $\displaystyle a=x$ does not.

5. (Already seen 2 posters posting the same question, interesting)