- Thread starter
- Banned
- #1

- Thread starter Poirot
- Start date

- Thread starter
- Banned
- #1

- Jan 29, 2012

- 661

For $1\leq x <y<+\infty$ you'll getf:[1,infinity)->[1,infinity) $f(x)=x^{0.5}+x^{-0.5}$ I thought about using MVT but it doesn't work and I've tried showing it conventially but i can't reduce it to k|x-y|

$\left|f(y)-f(x)\right|=\dfrac{1}{2\sqrt{c}}\left(1-\dfrac{1}{c}\right)|y-x|$

Now, use that a global maximum for $F(c)=\dfrac{1}{2\sqrt{c}}\left(1-\dfrac{1}{c}\right)$ in $[1,+\infty)$ is $K=\dfrac{1}{3\sqrt{3}}<1$