suppose f and g are continues on [0,1]
and differentiable on (0,1)
and f'(x)g(x) differs f(x)g'(x)
for every x existing in (0,1)
prove that there is a point c in [0,1] so g(c)=0

??

for what purpose do i need to know that
"f and g are continues on [0,1]
and differentiable on (0,1)
??"

g(c)=0 is the use of MVT

i dont know how to merge the peaces
??