Does the value of the second derivative related to the 'a' in a normal quadratic equation since the 'a' represents the shape of the curve whether its concave up or concave down?
Kelvin, thanks for the question. Good observation; the "a" in the quadratic function will be relevant in a couple of ways. Firstly, before even differentiating, it tells you the concavity of the parabola (positive a = concave up, and vice versa). Secondly, the value of a will be relevant to the extent of being a value that will multiply by 2 for the first derivative (x^2) and then the product of 2 and "a" being the constant for the second derivative. This means that if "a" was a number like 3, then 2 x 3 = 6 will be the second derivative for a quadratic function. So "a" multiplied by 2 will give you the constant second derivative for a quadratic function! E.g. f(x) = 3x^2 + 5x + 7 F'(x) = 6x + 5 F''(x) = 6 Note that a = 3 and 2 x 3 = 6
Imagine the graph was shifted up so that both of the turning points sit ABOVE the x-axis, meaning that the y-value is positive for the maximum AND the minimum turning points. We must therefore look at the concavity of the graph at those points to determine whether it is a maximum (negative - concave down) or a minimum (positive-concave up). Hope this helps. If you need further explanation, let me know.
Will Banks also, if the second derivative at a turning point is positive, it is a MINIMUM because the curve is facing UP, meaning around that point, the graph gets higher, not lower.
Ola Cierpiol What do you mean by "ordinary level". This is one of the most useful ways to find maximum and minimum values for graphs and worded problems, using the second derivative to prove whether something is a maximum or minimum. Thanks!
thank you love your video but i looked at it to help with this particular math problem that i cant solve it says find all turning points to the nearest tenth in the function X^4-4x^3+2X^2+x+4 and i cant find it some one please help =(
@@claraishungry501 Hey thanks so much, I’m better now finished maths a while ago now aha. Hope everyone watching this vid is doing better than when was watching it.
Hey, thank you so much this really helped me! What helped the most was that you explained the little bits the books usually leave out.
No worries! Glad it helped :) Spread the word!
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perfect, and i like his reprimanding tone o voice, suits my slow-understanding and stupidity
Hahaha
Great video. An easy-to-follow explanation not too long either. Really helped me with the topic.
Keep people with relevant videos, watch how to find maximum and minimum turning points of a function : ruclips.net/video/nvTW4ZTTxTo/видео.html
bad quality video but high quality teaching, thanks a lot mate
Thanks so much! Really helped with my GCSE further maths
Thank you a lot! So clear and helpful explanation. I was so glad when I came across this video lesson. Great job!
I had been out of university for 5 years and my memory has come back with your video thanks man you should have more 👍 up
well explained....thank you.
Tomorow is my final exam, and by watching this vedio I am very clear about the concepts, thank you so much 😊
great work, easy to understand and v helpful for my exam thanks
Very clear video, helped that you mapped it out on the graph step by step. good video thanks
This was the most helpful video I’ve seen. However try to use a wider screen so everything is clearer ok 👍🏻 😊
Yes, Thank u! You said all i was looking for! Than man again that means a lot!
Thank youu Thank youu! My brain was hurting and I had to watch like 7 different vids and this is by the BESTT!
came from a book that puts the link of this video in...understood immediately
Thank you, man! You explain very well! Very helpful
Extremely helpful, thank you so much for your help! :')
Such a very good explanation....
Is concave up concave down in australia?? Concave down under??
Is this curve right?
Looks like a Sin(x) curve
Does the value of the second derivative related to the 'a' in a normal quadratic equation since the 'a' represents the shape of the curve whether its concave up or concave down?
Kelvin, thanks for the question. Good observation; the "a" in the quadratic function will be relevant in a couple of ways. Firstly, before even differentiating, it tells you the concavity of the parabola (positive a = concave up, and vice versa). Secondly, the value of a will be relevant to the extent of being a value that will multiply by 2 for the first derivative (x^2) and then the product of 2 and "a" being the constant for the second derivative. This means that if "a" was a number like 3, then 2 x 3 = 6 will be the second derivative for a quadratic function. So "a" multiplied by 2 will give you the constant second derivative for a quadratic function!
E.g.
f(x) = 3x^2 + 5x + 7
F'(x) = 6x + 5
F''(x) = 6
Note that a = 3 and 2 x 3 = 6
surely if the y value is positive it will be more than zero (as you said) but that would make it a maximum because it is positive...?
Imagine the graph was shifted up so that both of the turning points sit ABOVE the x-axis, meaning that the y-value is positive for the maximum AND the minimum turning points. We must therefore look at the concavity of the graph at those points to determine whether it is a maximum (negative - concave down) or a minimum (positive-concave up). Hope this helps. If you need further explanation, let me know.
Will Banks also, if the second derivative at a turning point is positive, it is a MINIMUM because the curve is facing UP, meaning around that point, the graph gets higher, not lower.
Thank you this helped a lot.
why can’t we just see the y value of the turning points and the greater is the maximum point and smaller is minimum
That is an insane explanation
Good one
super explanation
thank you sooo much
That was fantastic , keep going 👍
Thank you so much 🤩😇
Thank you so much for providing such an excellent and comprehensible class. I have learned a lot from it :-)
Thank you so much! Really glad this helped, my friend :) I hope to have more videos in the near future!
Thank you so much to share .
Realllly thank u sooooo much sir❤️
This was really really really helpful. Thank you.
Thnk u you've really helped me out
great vid keep it up
is this for ordinary level ?
Ola Cierpiol What do you mean by "ordinary level". This is one of the most useful ways to find maximum and minimum values for graphs and worded problems, using the second derivative to prove whether something is a maximum or minimum. Thanks!
EasyMath SC level
no this is for a level
This is for Advanced level mathematics (A levels) ,pure mathematics (paper 1)
Interesting 🙂
Really great video friend, thank you.
thanks brother
u the man
All good man! Thanks for watching
hey man you are doing a great job thanks alot:)
tt ff thank you so much! Glad it helped :)
@@jeddle bruh ur not the creator
Markee F woops, this is my other account (English videos)!
thank you love your video but i looked at it to help with this particular math problem that i cant solve it says find all turning points to the nearest tenth in the function X^4-4x^3+2X^2+x+4 and i cant find it some one please help =(
Great revision :)
helped a ton :)
Thank you sir
it is really helpful. really thz man.really thz
That's awesome! Thanks for watching :) Hopefully soon i'll be releasing some more videos on Calculus!
Who else doing exams 😭
Zion Wickham idk
Thanks much my honor 🙏
Thank you my son
Apart from only 240P brilliant video - as others have said fills in those little missing bits
Thankyou very much, this was so helpul
No worries, good luck!
Thank you
thanks a lot ,Great job
🔥
Thank youuu...
I want to cry
i know its been 2 years but are u okay now
@@claraishungry501 Hey thanks so much, I’m better now finished maths a while ago now aha. Hope everyone watching this vid is doing better than when was watching it.
@@emily-jaynestenson9343 Oh.. im glad then 🥺 and good luck with the rest of your journey!! :)
ty
THANK YOUOYUOYUOUYO
The gradient at the turning point is your girl
Get it? Cus its flat
big breast fill a man hand, but the flat one fill man heart
Fery McPhee not necessarily👀
Damnn thanks m8 I learned more than my 12 years in school 😂😂😂😂
Azhan Tariq 😂
So not funny , r u 5?
I can't see anything from ur hands wtf