Horizontal Asymptotes We need to assess the value of the function as We use the notation: lim f (x) and lim f(x) N.B. lim - =0 and lim - =0 x -> - x -> too X x -> - 0ox The horizontal asymptote for any polynomial can be found by writing it so that the highest degree is a factor.If y = f(x) has a critical point at x = c, with f'(c) = 0, then the behaviour of f(x) at x = c can be analyzed through the use of the by analyzing as follows: a. The graph is concave up, and r = c is the location of a local minimum value of the function, if f"(c) > 0. local minimum f (c) >0 b. The graph is concave down. and x = c is the location of a local maximum value of the function, if f"(c) 0 120 -+ + f' <:0eg.1: find the critical points for following functions. determine whether functions have a local maximum or minimum. f b eg.2: discuss function y="with" respect to concavity and of inection. x2>