Concavity, Inflection Points, and Second Derivative

[@TheOrganicChemistryTutor]

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Thank you for your amazing video. I have some question. So, in the last explanation the function is concave down on (1, 5) or (1, 5) except 4?

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[@ninegames4568]

So when you let the first derivative equal to 0 you get the max and min points, and when you let the second derivative equal to 0 you get the point of in inflection. Am I correct? Please correct me if I'm wrong

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Do we have to show the numbers that we are taking to know whether that number shows Positive sign in the number of negative sign ?

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[@nomi98]

You can't really say it is concave up on the union of those intervals (at 9:51), rather it is concave up on both of them separately.

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[@zainabhaider4369]

maybe a question. Why do we derive twice! We do not equate the first derivative with zero, as in Rolle's theorem.!! Why do we derive twice and not 3 or 4 times?.