Sketching a graph based on certain conditions.... Hello, I'm supposed to sketch a graph of f based on condtions I'm given. However some of the conditions I'm given I'm not sure exactly what is supposed to happen. A little help would be greatly appreciated. Here are the condtions, some of which I think I know what f is supposed to do, some I do not: [itex]f'(1) = f'(-1) = 0[/itex] : Does this mean there are horizontal asymptotes at y = 1 and y = -1? [itex]f'(x) < 0[/itex] if [itex]|x| < 1[/itex] : I believe f is decreasing here on (-1, 1) [itex]f'(x) > 0[/itex] if [itex]1 < |x| < 2[/itex] : I believe f is increasing here on (-2, -1) and (1, 2) [itex]f'(x) = -1[/itex] if [itex]|x| > 2[/itex] : I don't have any guesses for this one. [itex]f''(x) < if -2 < x < 0[/itex] : I believe f is concave down on (-2, 0) inflection point (0, 1) : I believe concavity changes at this point. Any help would be greatly appreciated.