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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

??