Hey folks, I haven't the foggiest idea how to start this problem. A tip or push in the right direction or link to a resource that explains these types of problems would be just great.

I've only done problems with the Mean Value Theorem of the form "Find 2 roots of $\displaystyle f(x)$ and comfirm that $\displaystyle f'(c)=0$ at some point $\displaystyle c$ between those roots.a. Use the Mean Value Theorem to show that for $\displaystyle 0<x<y$,

$\displaystyle \sqrt{y}-\sqrt{x}<\frac{y-x}{2\sqrt{x}}$.

b. Use part (a), above, to conclude that for $\displaystyle 0<x<y$,

$\displaystyle \sqrt{xy}<\frac{y+x}{2}$

Even just a hint or link would be great, thanks guys.