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 November 12th, 2012, 10:16 PM #1 Newbie   Joined: Oct 2012 Posts: 11 Thanks: 0 Determining graphs with cont functions My question asks me to select a graph that fits this description, however I keep getting it wrong. I know that I'm to pick a graph with 1 critical point, and that vertical tangent lines count as crit. pts, but My first two selections were wrong... Question: How would graph look like If f is a continuous function on (?4, 4) such that (a) f has exactly 3 critical points, (b) f has exactly 1 local maximum, (c) f''(x) > 0 on (?4, ?2), (d) f''(x) < 0 on (0, 2), (e) (0, 1) is an in?ection point, (f) f'(x) < 0 on (2, 4).
 November 13th, 2012, 10:10 PM #2 Senior Member   Joined: Aug 2012 From: New Delhi, India Posts: 157 Thanks: 0 Re: Determining graphs with cont functions What do you mean by a critical point? Do the 3 critical points include the local maximum? And if you have options, it's better you take a picture of the question sheet and upload it to some image posting website and link it here. Here is a recommended website to do so http://imageshack.us/
November 14th, 2012, 12:22 PM   #3
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Re: Determining graphs with cont functions

Quote:
 Originally Posted by allylee My question asks me to select a graph that fits this description, however I keep getting it wrong. I know that I'm to pick a graph with 1 critical point,
Why do you say "1 critical point" when a condition below says "f has 3 critical points?

Quote:
 and that vertical tangent lines count as crit. pts, but My first two selections were wrong...
The condition that the function be continuous forbids vertical tangents.

Quote:
 Question: How would graph look like If f is a continuous function on (?4, 4) such that (a) f has exactly 3 critical points, (b) f has exactly 1 local maximum, (c) f''(x) > 0 on (?4, ?2), (d) f''(x) < 0 on (0, 2), (e) (0, 1) is an in?ection point, (f) f'(x) < 0 on (2, 4).

March 8th, 2013, 08:01 AM   #4
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Re: Determining graphs with cont functions

Quote:
 Originally Posted by HallsofIvy The condition that the function be continuous forbids vertical tangents.
No, it doesn't.

Quote:
 Originally Posted by allylee My question asks me to select a graph that fits this description
Does it? Or does it provide a graph and ask you which criterion is NOT satisfied? If the latter, the answer would be that there are not exactly 3 critical points.

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