What are the critical numbers of f(x) = (x2+3)/(x-1) I took the derivative and found f'(x) = (x+1)(x-3)/(x-1) so I thought the critical numbers were 3, ±1 ...sadly, this is incorrect. I always thought the definition of a critical number was where f'(x) = 0 or DNE. But for this to be applicable, must the value for x firstly exist in the domain of f(x) or not? Since for all values of x not in the domain of f(x), it would also not exist in f'(x) and that includes vertical asymptotes. So are values for vertical asymptotes not considered critical numbers?