I have read over both of my math texts many times, I am just really having difficulty with this concept. I understand the theory behind it, that if a function satisfies the two conditions then the slope of the tangent = f'(c) for some c on the interval of the function (a,b), but having a hard time apply the theorem.

so what I am up to now is that y-x/2sqrt c < y-x/2sqrt x

So just as long as x is larger than 0 and c is larger than x it should work for any numbers?