2nd derivative test, a visual explanation

Note: at 1:38 I said that a cubic is an example of a point of inflection that doesn't seperate concavity. This is rubbish, as it actually does. So please ignore that 5 second snippet of dribble.
Explain visually what the 2nd derivative does to a function, and how using it determines the nature of stationary points.

[@ashleyklein9822]

This is the only video that was able to get me to finally understand how this works ... thank you!!!

[@BrianAmedee]

No worries. Concavity is a tricky concept without a visual

[@ln_cript]

I know that you arent active anymore, but im sure you still watch youtube! This video is incredible, I usually have to spend a few days thinking on something deeply to get this kind of intuition. A few weeks ago I was trying to understand this until the pieces to the puzzle finally started to become visible. This definitely solidified my understanding, cant wait to watch more of these when I learn integration! That'll be tough!

Incredible video, a shame it has so little views. Thank you!

[@dhoomketu731]

beautifully explained! thankyou!

[@PamelaGuzman-jv5yt]

Dear Brian Amedee,
Thank you for caring about the fundamentals of calculus, and thank you for your attention to detail. The world needs more people like you ♥

[@tahatariq73]

This is the exact thing I was looking for. Thank you 🎉

[@ioerror2077]

Finally a way i can adjust this thing in my head. Thanks 👍

[@Boyyyyaan]

amazing video. im surprised it only has 140 likes. thank you so much

[@madebyarmadillo]

What software is used to produce these visuals? I have a TA who has shown similar-looking work. It helps me tremendously, so I would like to know... thank you for the detailed explanation!

[@TheFlyingBird]

Goat

[@mike_astro]

I love you, thank you

[@weshare-7days]

Can you share the code manim? Sir

[@BrianAmedee]

Yeah! Message me in discord so I can send you the file!

[@weshare-7days]

@@BrianAmedee TFV_Fujiko#2668, please send for me! Thanks sir

[@BrianAmedee]

@@weshare-7days send you a message

[@SlaveOfAllah12342]

Thanks alot dude

[@vinhvo6001]

Can you share the code manim sir?

[@BrianAmedee]

Yeah, message me in discord. I am happy to share. However, the syntax is very outdated.

[@vinhvo6001]

@@BrianAmedee Thank you so much.