Quandaries
and Queries 

I am trying to solve an existence of fixed point problem. I need to show that a function f (on reals) with f'(x)=>2 has a fixed I started off with g(x)=f(x)x and the mean value theorem on g, and
need I wish to show g(x)>0 for some x, and g(y)<0 for some y. And then
by But I am not able to show g(x)>0 and g(y)<0 for some x, y. Can you help? 

Hi Bob, g'(x) = f'(x)  1 >= 1, so g(x) goes to  infinity when x goes to  infinity, (by the mean value theorem, g(x) <= g(0)  x for x positive) and g(x) goes to infinity when x goes to infinity. This should help. Claude 

