this guy has been carrying me since sophomore year in High school (chemistry) then junior year (algebra & chemistry) then senior year (calc 1 and physics) then 1st year of engineering in a few classes and now in second year of engineering. YOU ARE A LIVING LEGEND!
Your channel is so helpful, I don't even go to the lectures anymore. I just watch your 15-30 min videos and it saves me 2 hours of commuting to and from uni only to attend a lecture I don't gain anything from.
im not gonna lie, math been having me fight for my life in the arena for the last couple weeks. thank u so much for this video. gonna secure atleast B because of your help. u a real one.
IDK who you are but I hope your beautiful TH-cam videos are letting you live life on a yacht somewhere in the Caribbean. You are amazing bro. I'm going to university where I get hella confused, and come home to watch your videos which are AMAZING and help me understand the content more. Nothing but love bro!!!
Professor Organic Chemistry Tutor, this is another fantastic video/lecture on Local Extrema, Critical and Saddle Points in Calculus Three/Multivariable Calculus. The problems associated with this topic are messy/problematic from start to finish. Once again, thanks to the great viewers for finding and correcting the error at the 6:04-minute mark in the video.
@@pjk7685 Yes, the other examples are correct. Notice how he contradicted himself later saying that fxxfyy - fxy > 0 meaning that it's a local min (which it is). Only the first example is incorrect.
how did he find those three points at the last problem (14:34) (0,0) (1,1)(-1,1) . I know that he said plug in 0 ,1,-1 but I'm not sure why he did that.And where did he get those values to plug in
6:07 Why did we say this point is local min , and the rule says if the second derivative is negative , it will be local max ? + Thank's so much on your effort.❤❤
@@sadhiyausama9504 Those points aren't valid, as the fx value for f(8,2) would be 8(8^3-2)= 8(510) =/= 0 Only the fy value would be 0, 8(2^3-8) = 8(8-8) = 0 Only points that make both the derivatives 0 work The reason why f(-1,-1) works is because fx = 8(-1^3-(-1))= 8(-1+1) = 0 fy = 8(-1^3-(-1))= 8(-1+1) = 0
The method isn't shown, but you just solve for a variable in the 1st equation and substitute for it in the 2nd so you only have an equation with respect to a single variable. Like this: First, our initial equations are: [1] 8(x^3 - y) = 0, [2] 8(y^3 - x) = 0 We can divide equation [1] and [2] by '8' on both sides, as they equal 0. This will simplify stuff. [1] x^3 - y = 0, [2] y^3 - x = 0 Let's try solving [1] for y: -> x^3 - y = 0 x^3 = y Well that was easy, wasn't it? Now we substitute for 'y' in equation [2] with the new value. [2] (x^3)^3 - x = 0 x^9 - x = 0 < [Factor] > x(x^8 - 1) = 0 Now to solve this, we have 2 solutions: (1) x = 0, (2) x^8 - 1 = 0 Since the exponent on 'x' in (2) is even, both x = 1 and x = -1 are solutions. Now finally to get their respective 'y', just plug it back into our original substitution. (1) x = 0, y = 0^3 = 0 (2) x = 1, y = 1^3 = 1 OR x = -1, y = (-1)^3 = -1 So our points of interest become: (0, 0), (1, 1), (-1, -1), as they are the only ones which satisfy both equations. They are the only possible critical points for the function. To figure out whether they are relative/local extrema, or simply saddle points, we use the double derivative test!
I had some fun trying to graph this multivariable function from 7:05 and got this on Geogebra: 'imgur a 48VnSO7' (youtube comments aren't so nice with links, put a 'forward slash' between the 'com' and 'a' and the value. Remember that 'com' goes after imgur. I noticed that the local minimum points reach '8', as calculated for both f(1,1) and f(-1, -1), but how come the graph intersects the z-axis at '12' instead of the '-64' we calculated through f(0, 0)?
Thank u very much sir... God bless you Sir i will need videos on differentiatial equation and partial differentiation from first principle of multivariable.. can u help please
No he doesn't substitute the x into y . He is taking partial derivative in terms of y from fx function which is f(x) = -6x +12 if we take partial derivative in terms of y for this function mean we will be getting 0 because there is no y value to differentiate
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Fxx=-6 ; Therefore it is local maximum as Fxx
Yes I agree
yes
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this guy has been carrying me since sophomore year in High school (chemistry) then junior year (algebra & chemistry) then senior year (calc 1 and physics) then 1st year of engineering in a few classes and now in second year of engineering. YOU ARE A LIVING LEGEND!
agree!! and i started my engineering with these lectures
@@aswininaidu same here. He's been there for me since my AS and A'level days.
this guy has saved my life countless times. Im not even religious but god bless you
You know dude,it's not even good to be proud that you are not religious
If there is no god according to you then how you came into being
@@jahanzaibali7852 how come god came into being?
Lmao i knew low iq fucks would reply to you all butthurt lmaoo
Saying you are not religious is the worst thing you can say on the internet
5 hours before my calc final. i owe this man my life 🙏
2 hours before mine lol
@@Trump_Gaming 1 hour lol
@@aadiliqbalkhan8216 How did it go?
3 hours before my final🤧🤧
@@cindysee4626 Good luck! Tell me how it goes. Mine was kinda BS but I passed.
Your channel is so helpful, I don't even go to the lectures anymore. I just watch your 15-30 min videos and it saves me 2 hours of commuting to and from uni only to attend a lecture I don't gain anything from.
same here
Sounds like I wrote it myself
You have saved me countless times in all of science and math, although you have an error which everyone is pointing out. You are the best
ur tutorials never failed to rescue me from dicey situation. Cant thank you enough
For problem one it should be local max. D < 0 and fxx(a,b) < 0 , then f(a,b) is a local maximum.
D > 0*
Yeah, I noticed that too
What can you happen
I love you man. You saved me before my exams in college and now I am in University and I am still learning from you. #BestTutorinTown
im not gonna lie, math been having me fight for my life in the arena for the last couple weeks. thank u so much for this video. gonna secure atleast B because of your help. u a real one.
IDK who you are but I hope your beautiful TH-cam videos are letting you live life on a yacht somewhere in the Caribbean. You are amazing bro. I'm going to university where I get hella confused, and come home to watch your videos which are AMAZING and help me understand the content more. Nothing but love bro!!!
Professor Organic Chemistry Tutor, this is another fantastic video/lecture on Local Extrema, Critical and Saddle Points in Calculus Three/Multivariable Calculus. The problems associated with this topic are messy/problematic from start to finish. Once again, thanks to the great viewers for finding and correcting the error at the 6:04-minute mark in the video.
This guy has been carrying my education for the last 3 years
Shouldn't (2,2) be a local maximum? Since fxx is negative?
are the other examples correct? I dont want to study incorrect material....
@@pjk7685 I believe so.
Yeah thats correct
@@pjk7685 Yes, the other examples are correct. Notice how he contradicted himself later saying that fxxfyy - fxy > 0 meaning that it's a local min (which it is).
Only the first example is incorrect.
@@pjk7685 He may make a silly mistake while solving as any other human but he never teaches anything wrong and never will.
how did he find those three points at the last problem (14:34) (0,0) (1,1)(-1,1) . I know that he said plug in 0 ,1,-1 but I'm not sure why he did that.And where did he get those values to plug in
How is this youtube channel better than my school wtf am i doin with my life?
The future of society is dependent on the faceless man, WOW 🎉 You're the GOAT!
God bless you, you are a gift to Humanity!
I hope your beautiful TH-cam videos are letting you live life on a yacht somewhere in the Caribbean.
How do you find the points of interest though? When your partials have both x and y in them, I mean
Real
Solve the partials for 0 as a system of equations.
i dont usually write comments.....but i had to thank you....keep doing this
Aight imma watch this whole channel before finals lol
Just to remind you...
Yeah, same tbh. Better than lectures
organic chemistry tutor. carrying my maths degree since 2019
You are an amazing instructor!! been using your lessons for years now!
May God bless you. You got the prayer of many students. .
the point (2,2) should be a local maximum because fxx is negative and D is positive!
were are u from?
what does the letter D mean plz help???
@@imranahmed-mt8wg D --> second partial derivative test
@@imranahmed-mt8wg Discriminant or Hessian of function f
true
the organic chemistry teacher is an angel
p(2,2) is local maximum since D>0 AND Fxx
yehh
U are still the best educative TH-cam even at this unconscious mistake...
on the second question, how did you determine that those were the points of interest?
this
You first solve the two first partial derivative equations then you will find critical points from there
@@khiziiikhan how
I believe it is just a matter of figuring out what values to input into fx and fy to get zero which happen to be (0,0), (1,1), and (-1,-1)
literally more useful then my calc III professor
Calculus! Taking me back to the 80s-my university days.
P(2,2) is local max not min, u contradicted yourself.
2:25 yo that's actually helpfull thx, now I can imagine what's the local min, local max, saddle point! thank you again :)
ALL HAIL THE ORGANIC CHEMISTRY TEACHER
this man is my hero
the first math should be local maximum ,thnx,great video,huge fan,just doing my work,so that others can follow through
You're the GOAT. Thank you again Mr. Organic Chemistry Tutor. o7
I learned more from you than from the lectures of my professor.
If you could do triple integrals with finding the bounds, youll be a life saver
6:07
Why did we say this point is local min , and the rule says if the second derivative is negative , it will be local max ?
+
Thank's so much on your effort.❤❤
Caught that as well, I assume it was a blunder
yeah same, i changed my notes and then realized oh wait no... he is wrong
@@zeitgeistsandmicrocosms blunder :DDDDDDDDDDd
you saved my 3 hrs dude!! Thank you
his explanation burns in my mind
I wish you good health and may the good lord continue to bless your good work ❤️
On the second example, why do we chose (0,0) , (1,1) and (-1,-1) as our points of interest?
These points satisfy the two equation
If that is so, we can have points like (8,2) , (27,3).... also right? Do we need to consider points like these?
@@sadhiyausama9504 Those points aren't valid, as the
fx value for f(8,2) would be 8(8^3-2)= 8(510) =/= 0
Only the fy value would be 0, 8(2^3-8) = 8(8-8) = 0
Only points that make both the derivatives 0 work
The reason why f(-1,-1) works is because
fx = 8(-1^3-(-1))= 8(-1+1) = 0
fy = 8(-1^3-(-1))= 8(-1+1) = 0
@@trollguyawsomeness oh yeah!! Correct..I didn't think about fx..Thank you so much
The method isn't shown, but you just solve for a variable in the 1st equation and substitute for it in the 2nd so you only have an equation with respect to a single variable. Like this:
First, our initial equations are:
[1] 8(x^3 - y) = 0, [2] 8(y^3 - x) = 0
We can divide equation [1] and [2] by '8' on both sides, as they equal 0. This will simplify stuff.
[1] x^3 - y = 0, [2] y^3 - x = 0
Let's try solving [1] for y:
-> x^3 - y = 0 x^3 = y
Well that was easy, wasn't it? Now we substitute for 'y' in equation [2] with the new value.
[2] (x^3)^3 - x = 0 x^9 - x = 0 < [Factor] > x(x^8 - 1) = 0
Now to solve this, we have 2 solutions:
(1) x = 0, (2) x^8 - 1 = 0
Since the exponent on 'x' in (2) is even, both x = 1 and x = -1 are solutions.
Now finally to get their respective 'y', just plug it back into our original substitution.
(1) x = 0, y = 0^3 = 0
(2) x = 1, y = 1^3 = 1 OR x = -1, y = (-1)^3 = -1
So our points of interest become: (0, 0), (1, 1), (-1, -1), as they are the only ones which satisfy both equations. They are the only possible critical points for the function. To figure out whether they are relative/local extrema, or simply saddle points, we use the double derivative test!
you are one of the Best teachers.
hey friend, love your work always and forever but please check your solution to the first question. Should be local max.
Great and helpful video. Thanks. Keep the good work up.
@The Organic Chemistry Tutor, I think the example number 1, the point is a local maximum.
I really appreciate this video tho, thanks man, I'm gonna sub to this channel. Best of luck for you!
Where did you get points of interest in second problem 😢
I had some fun trying to graph this multivariable function from 7:05 and got this on Geogebra: 'imgur a 48VnSO7' (youtube comments aren't so nice with links, put a 'forward slash' between the 'com' and 'a' and the value. Remember that 'com' goes after imgur.
I noticed that the local minimum points reach '8', as calculated for both f(1,1) and f(-1, -1), but how come the graph intersects the z-axis at '12' instead of the '-64' we calculated through f(0, 0)?
his explanation is fab
Pls how do you get the numbers you plug in as 2 for the first question?
Could you do a video on sketching double and triple integrals?
Can you suggest me
My second lecture...first is my mother 😊
really helped for my assignment thanks a bunch
You are the best ❤
thankyou so much this helped a lot lysm omg
At 8:55, I'm having trouble understanding where the points of interest came from...I'll try rewinding a bit.
CORRECTION AT 6:04. IT IS A LOCAL MAX
May God bless your generation 🙌
luckily his old videos will help me
Hi, your videos have been very helpful and I thank you for it. but in the 2nd example....wouldn't -1^3 -1 = -2? which would then be 8 (-2) = -16?
Why are 00 11 -1-1 points of interest? Are they given or is it just what you use when dealing with a cubic equation?
We set f(x) = 0 and f(y) = 0, then we take out the two values that gives us f(x) = 0 and f(y) = 0 then use them as Points for D
You made a mistake fxx0 it's not local min but local max
Thank u very much sir... God bless you
Sir i will need videos on differentiatial equation and partial differentiation from first principle of multivariable.. can u help please
thankyou!!! you saved me
can you please make video for Cal3 Final review too????? Thank you!!!!
I love this man
4:24 isn't that F(2,2) suppose to be local Maximum since fxx
Bro you rocked
I think you confused on the example - when D>0 and f(xx)
Calc 3 looks fun. Yum.
Tackar som fan my friend
At 8:25, why is your point of intrest (0, 0)?
Thank you!!!
You are amazing, thank you.
Thanks ❤🌹🙏
Thanks ❤
why did you choose the points (0,0) (1,1) and (-1,-1) for the second problem?
did you know why??
Did u find out y?
You are a god. I appreciate all that you do
Once again, thanks !
u got a subscriber,thanks
Thank you soo much!
D > 0 and Fxx < 0 => Local Max
Thank you sir😘😘
Hi, can anyone please post a link on how to factor multivariable functions as the one used in the video in form of binomials e.g. (x-y)(x+1)(x-1)
is it possible for the local min or max be equal to zero, if so, whats the conclusion?
He's the best
Thanks man!
Where the face reveal at?? you been helping me all the way through college
Pleased i need the playlist of this video
Thank you sir.
Thank u 😭💜
BRO YOUR COMING IN FUCKING CLUTCH FOR MY CALC III EXAMS
at 5:07 how does he get fxy= 0? does he substitute the x into the y? sorry I am dumb
No he doesn't substitute the x into y . He is taking partial derivative in terms of y from fx function which is f(x) = -6x +12 if we take partial derivative in terms of y for this function mean we will be getting 0 because there is no y value to differentiate
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