Is a point of inflection concave or convex? - Which answer is correct?

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A point of inflection does not necessarily require the existence of an inflection point if the function has undefined areas. The discussion emphasizes the importance of analyzing the second derivative to determine concavity or convexity in different intervals. Some participants express frustration over the complexity of identifying these points, leading to confusion. It is highlighted that spending excessive time on such problems without clear solutions can be unproductive. Understanding the behavior of the second derivative is crucial for accurately determining concavity and convexity.
Sarah66
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Homework Statement
Hello everybody, :)
I have a problem with determining the intervals of convexity and concavity of this function:
Relevant Equations
there are no inflection points here for me
problem1.png

but for me there is no solution to this inequality...
I never wait for a ready answer but I've already spent 4 hours on it and I still don't know what to mark...
 
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Sarah66 said:
there are no inflection points here for me
There doesn’t need to be an inflection point to switch between concave and convex if there are points where the function is undefined.
 
Check the sign of the 2nd derivative on each interval if you aren't sure.
 
Thread 'Chain falling out of a horizontal tube onto a table'

Thread 'Chain falling out of a horizontal tube onto a table'

My attempt: Initial total M.E = PE of hanging part + PE of part of chain in the tube. I've considered the table as to be at zero of PE. PE of hanging part = ##\frac{1}{2} \frac{m}{l}gh^{2}##. PE of part in the tube = ##\frac{m}{l}(l - h)gh##. Final ME = ##\frac{1}{2}\frac{m}{l}gh^{2}## + ##\frac{1}{2}\frac{m}{l}hv^{2}##. Since Initial ME = Final ME. Therefore, ##\frac{1}{2}\frac{m}{l}hv^{2}## = ##\frac{m}{l}(l-h)gh##. Solving this gives: ## v = \sqrt{2g(l-h)}##. But the answer in the book...
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