Concavity, Inflection Points, and Second Derivative

[@TheOrganicChemistryTutor]

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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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[@pawanbhandari5512]

In 11:02 sec the interval of point of inflection might be (-15,-2), but except that you have done a great job.

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[@lanadelray9169]

A question : if we have second derivative equals zero only for x=6 for example and that is its (- 5 -) will then we say it’s convex for all real numbers or for all real numbers except 5

[@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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Me.

[@HabibUrRahman-sr2wn]

Now for the second example if i want to know the intervals on which graph is increasing or decreasing right from this diagram without even getting into the first derivative thing
How can i find increasing and decreasing intervals.
I saw your other video on that but that seems a bit hard...

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@TheOrganicChemistryTutor
I am totally confused that if we can find the local and absolut Maxima and Manima with the First Derivative Test then why do we use the second Derivative test? Isn't only the first one enough? Please explain.

[@sophiaw2195]

You don't need the Second Derivative Test, but it can be a faster way of determining whether the critical points are relative maxima or minima

[@stimulus7222]

Sec derv test is for the x coord of the inflection point

[@Shaz-oo8lq]

If there's a cusp at a point, and that point is between 2 concave ups, could we include the cusp in the interval of concave up for example a cusp at 0, but the interval of concave up is (-1,2)?

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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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