Concavity of a parametric curve

In this video, I showed how to evaluate the second derivative of a parametric function and also to determine on interval, it is concave up

[@kingbeauregard]

I figured out how to do the first derivative, but I was stumped on the second one. Thanks!

[@jan-willemreens9010]

... A good day to you Newton, Despite being busy for one last week, I cannot resist complimenting you on your explanation regarding the second derivative in this presentation of a parametric curve! A major stumbling block for quite some students I assist, so thank you very much for this clear explanation Newton; well done! You see that I'm still present in the background, following your projects in silence (lol) ... Thank you Newton and stay well math friend, Jan-W

[@PrimeNewtons]

Yay! Good to hear from you, my friend. Yes, it's been busy. Hope to get a break soon. Thanks for the support and feedback. Cheeres!

[@domanicmarcus2176]

i am just curious why the interval is not closed. Why did you leave the endpoints as not included, when at the beginning "t" includes both zero and 2 pi?