Calculus I - Concavity and Inflection Points - Example 1

An example of finding points of inflection and intervals where a function is concave up and concave down.

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[@TheInfiniteLooper]

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[@roman20mark62]

I want concavity for the points X= -1/2 ??

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[@joshuakusuma5953]

Is it possible to have two different x values which would lead to two different points of inflection?

[@TheInfiniteLooper]

+joshua kusuma yes. I'm sure I have at least one video on my channel of a function with more than one inflection point, if you wanted to see an example.

[@falchion3568]

the f''(x) would have to be a quadratic

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I understand very well

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[@iggythefool8770]

thanks for this and btw,
the f(x) got me

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[@Consolous]

Great video, I learned from another video the concavity and came for the inflection point, but I reinforced my understanding of concavity while watching your video. 2 birds on one shot :) thanks!

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Yeah, all the thank-yous, but why did he stop uploading?

[@prab99uk]

Hi great video, but one question: I understand here you are told there is a point of inflection so you can use f''(x) =0 to find this point. But if you just had that equation and were asked to prove it was in fact a point of inflection at x=2, how would you go about it? I'm aware that a point of inflection implies that f"(x)=0 but I also know that f"(x)=0 does not imply that it is necessarily a point of inflection.

[@TheInfiniteLooper]

Thanks. You'd do literally exactly the same thing. Although we knew ahead of time in this case that there was a point of inflection, we didn't know where or what it was and when we looked for it we didn't use the fact that we knew it exists.
If you're just told to investigate then you do all of the same steps. The only difference is it's possible to conclude that there are no inflection points.

[@prab99uk]

Oh ok, I understand it now thanks! Also is it worth using f'''(x) instead of doing this method for a point of inflection?

[@TheInfiniteLooper]

Sorry, missed the notification on this one somehow. I don't think so. I don't see how using the third derivative can be helpful when looking for points of inflection. For points of inflection you want to know where the second derivative is positive, negative, and zero. The third derivative basically only tells you when the second derivative is increasing, decreasing, or constant.

[@samson4958]

i think its good that you are doing question but make it more clear

[@astronwitt2215]

Thanks, does ciritical number is only for f'(x)=0?

[@TheInfiniteLooper]

Critical numbers are values of x where f'(x) = 0 or where f'(x) is undefined, but f(x) in this video is a polynomial and polynomials are never undefined.

[@SK-vt3fj]

Very good