# ❖ Concavity, Inflection Points and Second Derivatives ❖

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Concavity and Second Derivatives – Examples of using the second derivative to determine where a function is concave up or concave down.

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hey there! thanks for the videos, I was just wondering if anyone could explain to be what happened at 6:11 thank you!

words can't describe my love and appreciation, thank you man!!

I could not follow this at all :/ Especially at the factoring part. I am so slow 🙁

thanks

You see the only problem with these videos are the fact that you do not go through every single step. So for people who need every single step like my self we have a hard time trying to figure out what you did when you skipped one step. Literally do every single step. It would really help if you explain it step by step even the smallest step will make us lost. Thanks for the great help!

Perfect ! Thank you 🙂

Doesn't the [square root of (1/5)] equal the [(square root of 5) divided by 5]?

Honestly, I can't thank you enough. You've explained it so clearly!

Thanks bae. You helped me with my final

Why did you ignore the 6 being distributed across the (x^2 – 1) term when you set it equal to 0?

wait, why are you setting x=0 to the second derivative, are you not supposed to find the critical points of the first derivative?

What if you are given a function that if you get the second derivative, you end up with a constant?

Great explanation. Thank you so much.

calc 1 final tomorrow thanks bruv

I FUCKING LOOVEE YOUR VIDS MAN! thank u

i'm very sleep deprived rn and the car alarm fucked me up…. kept pausing the video and stopped hearing it and definitely thought i was crazy ahahah

I thought the critical numbers were only where the first derivative is undefined or equal to zero and within the domain of the original function

Very helpful!

Why did you ignore the 6 being distributed across the (x^2 – 1) term when you set it equal to 0?

what about inflection points?

Why if put the critical points into the second derivative is finding the min and max? I don't get that

Thank you so much for your videos Patrick, you've really helped me out!

god bless you!

My hero. Thank you!

What will happen if the critical point and inflection point has same value ? Help pls ~

boring. what if we plug all point in first equatin…

+patrickJMT Something I completely had forgotten when watching this video was the difference of squares and it took me a while to remember what I was supposed to do to factor that lol.

i love you man, when i graduate, im going to buy you a bottle. #truuuuuu

teach my calc class. sign up at http://online.missouri.edu/

What does he do around 6:28 . I understand up until that point where he finds the X's what is the theroum for separating the polynomial?

Concave up like a cup

Concave down like a frown

Let's see how I do on this final tomorrow 🙂