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