Upper Bound for the Error Using Linear Approximation Suppose that f is a function such that f is bounded on some interval centered at x a that is there exist positive real numbers K and u such that f z K for all az in I a u a u Then for every ro I we have that Efa ro Lfa zo f xo Ko al e Use the upper bound for the error in linear approximation to find an interval of the form T 6 6 contained in I 1 1 guaranteeing that Ero zo 1 whenever zo T