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Sketching a graph based on certain conditions... 
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#1
Nov2705, 05:15 PM

P: 187

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. 


#2
Nov2705, 10:32 PM

P: 187

Any suggestions at all would be greatly appreciated. I'm confident that I can draw the final graph, but it's just determining what f is doing based on the conditions given of f'(x) and f''(x).
Thanks in advance. 


#3
Nov2805, 06:38 AM

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Thanks
PF Gold
P: 39,510

The only yvalue you are given is that f(0)= 1 since we are told that there is an inflection point at (0,1). There are, of course, an infinite number of graphs, y= f(x), that satisfy these conditions. 


#4
Nov2805, 08:38 AM

P: 187

Sketching a graph based on certain conditions...
Thanks again, HallsofIvy. I appreciate you giving the extra explanations. They help me understand these concepts a little more.



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