BlackMamba
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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:
f'(1) = f'(-1) = 0 : Does this mean there are horizontal asymptotes at y = 1 and y = -1?
f'(x) < 0 if |x| < 1 : I believe f is decreasing here on (-1, 1)
f'(x) > 0 if 1 < |x| < 2 : I believe f is increasing here on (-2, -1) and (1, 2)
f'(x) = -1 if |x| > 2 : I don't have any guesses for this one.
f''(x) < if -2 < x < 0 : 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.
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:
f'(1) = f'(-1) = 0 : Does this mean there are horizontal asymptotes at y = 1 and y = -1?
f'(x) < 0 if |x| < 1 : I believe f is decreasing here on (-1, 1)
f'(x) > 0 if 1 < |x| < 2 : I believe f is increasing here on (-2, -1) and (1, 2)
f'(x) = -1 if |x| > 2 : I don't have any guesses for this one.
f''(x) < if -2 < x < 0 : 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.
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