suppose that f is continuous on (a,b). If f is also differentiable on (a,b), except possibly at a single point where lim_x-> f'(x) exists and is finite, prove that f is differentiable at and that f' is continuous at .
suppose that f is continuous on (a,b). If f is also differentiable on (a,b), except possibly at a single point where lim_x-> f'(x) exists and is finite, prove that f is differentiable at and that f' is continuous at .