let me ask you this one..

we got f(x), g(x), in both there is differentiation.

for all x, we know: $\displaystyle f'(x)*g(x) $ ≠ $\displaystyle g'(x)*f(x) $

we also know there are: $\displaystyle f(a)=f(b)=0$

we need to prove that there is a point 'c', in zone [a,b], which gives us g(c)=0.

please help !