Suppose that f : [0,1)---IR is continuous on [0,1), differentiable on
(0,00), f(0) = 0, and lim f(x) = 0 as x tends to 00. Prove that there exists a point c in (0,00) such
that f'(c) = 0.
Problem Suppose that f : [0,1)---IR is continuous on [0,1), differentiable on (0,00), f(0) = 0, and lim f(x) = 0 as x tends to 00. Prove that there exists a point c in (0,00) such that f'(c) = 0.