How do I prove the following theorem, using ONLY Rolle's theorem?
Suppose that for some real number a,
f(x) is continuous on [a, inf)
and f '(x) exists on (a,inf)
with f '(x)>0 for all x>a
Then f(x)>f(a) for all x>a
I think I'm right in saying that Rolle's theorem is;
if a function f of real value is continuous on [a,b], differentiable on (a,b) and f(a)=f(b) then there exists a C in (a,b) such that f'(C)=0
but how do i PROVE the above theorem from that?
Please help
Thank you