Let f be a real-valued function that is continuous on [0, 1] and differentiable on (0, 1) and let g be a function defined on (0, 1] by g(x) = f(x) == x. if f(0) = 0, $(") == and f(1) = 0, (i) show that there exists c ir such that g(c)=0.
(ii) determine whether the equation g'(x) = 0 has any real root in (0,1). justify your answer.