I was doing my HW and I encountered a problem that confused me greatly. I will try to show an image because the question gives a graph and asks us to find the inflection points for the curve on the f , the f', and the f''. So yeah. I am very confused and if someone could explain this to me then I would be greatful.
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Still $x=-3,-1$? The question says to state the $x$-coordinates of the inflection points of the curve below. – peterwhy Jun 04 '22 at 16:24
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It is a poorly written question IMO. – Jun 04 '22 at 16:28
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It just wants the x values for the inflection points. so at -3 there is an inflection point and at -1 there is an inflection point. – Mehmed Sahan Jun 04 '22 at 16:28
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@MehmedSahan Yes, so the $x$ values are $-3, -1$. – peterwhy Jun 04 '22 at 16:29
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yes and then it ask to find the inflection point for the first and second derivative of the graph and I am confused on how to do that. I can find the derivative of an equation but I don't understand how I would do that for a graph. – Mehmed Sahan Jun 04 '22 at 16:32
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@MehmedSahan What I read from the question is to state the $x$-coordinates of the inflection points of "the curve below". Whether the curve is the first or the second derivative of something else does not seem relevant. – peterwhy Jun 04 '22 at 16:38
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so you are saying that they would all be x= -3,-1? – Mehmed Sahan Jun 04 '22 at 16:43
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so I just input that and it didn't work. I think that the derivative is relevant because it asks for the inflection point for f then f' then f''. – Mehmed Sahan Jun 04 '22 at 16:48
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1@MehmedSahan Maybe the first line of the question is instead asking for "the inflection points of $f$"? I only see one blue curvy line that may match "the curve below". – peterwhy Jun 04 '22 at 16:56
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I know that f is the graph. I know there are ways to find the f' and f'' just from a graph but everything I have found online makes no sense to me. Thank you for the help though but I think I will need help elsewhere for this specific problem – Mehmed Sahan Jun 04 '22 at 17:00
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Ok so I did some searching and I found that the inflection point for the given graph is where the graph changes its concavity. For the f' of the graph the inflection points are the max and mins of the first graph. for f'' the inflection points are where the first graph changes from negative to positive or where it changes from positive to negative. This actually works. – Mehmed Sahan Jun 04 '22 at 17:28
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1"I know that f is the graph." Actually, parts (b) and (c) explicitly contradict that statement. Taken at its absolutely literal meaning, part (b) asks for the inflection points of the graph of $f'$ assuming that $f'$ (not $f$) is shown in "the curve below". But I think you have correctly guessed the intent of the person who wrote the question; they just did a very poor job of translating their intent into words. (In particular, they unambiguously said things they didn't want to say.) – David K Jun 04 '22 at 18:53
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I am answering my own question in case anyone else has the same problem as me and needs help solving it. The inflection point for the given graph is where the graph changes its concavity. For the f' of the graph the inflection points are the max and mins of the first graph. for f'' the inflection points are where the first graph changes from negative to positive or where it changes from positive to negative.
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1The thing to take away from this is that sometimes the people who write these questions mess up. What they evidently meant to ask was, "State the $x$-coordinates of the inflection points of the graph of $y=f(x)$ under the following assumptions about the (possibly different) curve that is shown below." We can guess that's what they wanted because the question they actually asked is silly. – David K Jun 04 '22 at 18:59