$$F'(c)= 0 , a<c<b$$ $$=>0=f'(c)\frac{f(b)-f(a)}{b-a}$$ $$=>f(b)-f(a)=(b-a)f'(c)$$
I am confused. Above sum is written in my book. But, multiplication with 0 is forever 0. I am thinking how $b-a$ moved to left. And, while $f'(c)$ had to move to denominator of LHS. But, it moved to numerator. How? I was watching a tutorial on Mean Value theorem. He wrote that
$$f'(c)=\frac{f(b)-f(a)}{b-a}$$
Did my book mistake?