I think it would be better if it was called pringle...
@dreamscapeai75 жыл бұрын
Yeah, but the term saddle was coined before a pringle was manufactured
@ahmedaj20003 жыл бұрын
that's what i was thinking too lmao
@ajmackewicz2 жыл бұрын
Student on a test: "And there is a pringle point at (0, 0)." Professor: *visible confusion*
@YLprime2 жыл бұрын
pringle engineering
@shawezonline Жыл бұрын
Pringle shape was derived from concept of saddle point
@ricardovaras46675 жыл бұрын
This is just gold for me, I promise that when I get a job and (some) money I'll give it all (well, maybe not all) to Khan Academy, it's not just that you're helping me on College, you're also motivating me to follow some sort of a dream that I have. I'm so thankful with these and other content creators who want to share it's knowledge to everyone who wants to learn. (Also, sorry if I have errors in my grammar, non native speaker)
@llllllllllllllllllllllllIIIIl1 Жыл бұрын
how are you doing
@kibme5189 Жыл бұрын
The time has come to honor your promise! In other words it is time for you to pay up buddy.
@KSM94K11 ай бұрын
Okay time to pay now, not sure if you're with us
@SpeaksYourWord8 ай бұрын
@@kibme5189 Lmao he disappeared
@abhaypratapsingh60677 ай бұрын
u alive my frnd ? pay the bill then
@mohitkalra93293 жыл бұрын
The visualizations are pure gold!
@zairaner14897 жыл бұрын
The statement "If the derivative is zero in a point in singlevariable calculus, it is either a minimum or a maximum" is obviously false because it could happen that the second derivative is also zero -like the point 0 for x^3
@Jojo-hz6rk6 жыл бұрын
Raphael Schmidpeter Yep. And it's called a point of inflexion.
@nickmilkshake26616 жыл бұрын
Agreed
@surajitdasgupta25404 жыл бұрын
You guys are really great
@LayneSadler2 жыл бұрын
you missed the word "local"
@carultch Жыл бұрын
That's why the 2nd derivative test is inconclusive, when the determinant of the matrix is zero.
@zyzhang11305 жыл бұрын
For one variable case it is actually possible for a tangent plane to be flat for neither maximum nor minimum (inflection) 4:36
@damian.gamlath6 жыл бұрын
I wish Grant could go through and refresh all of Khan's older videos - Grant's stuff is just simply brilliant.
@ozboomer_au6 жыл бұрын
As an engineer, I find this sort of mathematics makes me *grin* (and bends my brain)... particularly when you look in terms of data structures in (computer) programming. In 2D (a "table" array), the X-variable and the f() (or Z) can have 'obvious' maximum and minimum values... in 3D (a "cube" array of 3 items), both the X-variable AND the Y-variable can be a maximum AND/OR a minimum... but you only realize this because you can see what's going on from a 3D viewpoint. What happens when we start thinking in 4D and beyond!? Time to re-visit 'Flatland' by Edwin A Abbott...
@sankaracharyadutta94087 жыл бұрын
Hey Grant !! Regarding your statement of Saddle points is a new concept in Multi -variable calc and the example about the single variable calculus --- In single Variable Calculus there exists a point called the POINT OF INFLECTION where the tangent has zero slope but it is neither a maxima nor a minima.. INFLECTION points are similar to saddle points because in such points the neighborhoods have different tendencies just like the fact that the partial derivatives have different tendencies here. So please Refer. But by the way you are doing a fantastic job by making the viewers really understand the topics through real 3d graphs... THANKS!! lots of love...
@zairaner14897 жыл бұрын
Exactly. Like x^3
@stephenbeck72225 жыл бұрын
Inflection points in single variable generally are not where the first derivative is zero. That’s the difference.
@234pg7867 жыл бұрын
Solomon Khan I owe you my life I kept trying to visualize and draw what a saddle point would look like today in class with no luck. The 3D graphics really help
@AdityaFingerstyle7 жыл бұрын
The instructor in this tutorial is not Sal
@robertcharmers32647 жыл бұрын
As ever, an adequately comprehensive and clear exposition of a relatively involved topic. Many Thanks.
@mrapter78 жыл бұрын
How does one person know so much?
@pt-ri4ng7 жыл бұрын
Khan Academy
@liabraga46416 жыл бұрын
3blue1brown actually
@shivkarj14563 жыл бұрын
Both
@giantneuralnetwork8 жыл бұрын
Always heard of saddle points... A local min and max! It's like you're close to a local max and yet so far away. Darn saddle points...! These vids are great, thanks for making them.
@iwtwb87 жыл бұрын
For everyone commenting about whether saddle points are new concepts or not- I see what you mean but I think he is talking about cases were where the second derivative is not zero. IE, the function he is displaying has a negative second derivative with respect to y, but a positive second derivative with respect to x. That is the new concept.
@venjaminschuster27972 жыл бұрын
Khan academy is my new Netflix! Love it! Thank you very very much!
@pavanpatel67587 жыл бұрын
what is the software, you are using for the graph?
@TheAcujlGamer4 жыл бұрын
Python
@wildertapiasaenz23333 ай бұрын
These graphics are awesome and help so much conceptually, thank you! 🙏
@tahoon20096 жыл бұрын
That's a beautiful visualization, thanks :)
@Quantum_Dots4 жыл бұрын
3B1B is here!
@worldfromhome40332 жыл бұрын
Great visualisation
@clapathy2 жыл бұрын
such a clear description of the saddle point
@Persian7717 жыл бұрын
awesome what a beautiful graph It makes it easy to understand.
@Savvy07 Жыл бұрын
That's the voice of 3 blue 1 brown
@ShokhanBirlikov7 жыл бұрын
3blue1brown?
@ranjeetthorat13184 жыл бұрын
y=x3 − 6x2 + 12x − 5 at x=2 => saddle point ...
@poojamittal41485 жыл бұрын
Thank you so much sir I was unable to understand saddle point before. Thank you for teaching me.
@MayankGoel4472 жыл бұрын
I kind of disagree with Grant, the point of inflection in single variable calculus is very similar to the saddle point, e.g. f(x)=x^3 f'(0)=0 but the origin is neither a maxima nor a minima. Both require computing second derivative
@sin3divcx2 жыл бұрын
Great explanation! May i ask you what program you are using?
@miguelmendoza42744 жыл бұрын
What software do you use to do this???
@semih84485 жыл бұрын
very good explanation, thanks!
@haraldlindohf40324 жыл бұрын
*Cries in inflection point*
@SiddharthSingh-zd7ny3 жыл бұрын
Very insightful
@Troy-ol5fk2 жыл бұрын
this 3d graphic is cool
@gurleenkaur96016 жыл бұрын
Great inituitive video 😊
@edward7282 Жыл бұрын
So basically saddle points have replaced stationary points of inflection (X=0 for stuff like y=x^3) in the 2D world. Interesting
@shreyasarkar42203 жыл бұрын
How are plateaus treated in maxima and minima? When are they considered an extrema point?
@anhminhtran74366 жыл бұрын
Awesome Videos!!! Thanks a lot Khan :))
@photon27245 жыл бұрын
they should rename it to 'pringle points'
@diastema72247 жыл бұрын
could you say that saddle point is a point equilibrium between the x and y planes?
@MCERUTUJAPATIL3 жыл бұрын
At 4:39 your sentence is wrong... Because in x^3 at x=0 there is no local maximum not local minimum..... But it is a critical point...
@toja83236 жыл бұрын
What about f(x)=x^3, then f'(x)=3x^2 and for x=0 f'(x)=0. Is it a saddle point, because it isn't local maximum or minimum?
@harryloo0073 жыл бұрын
When you end up coming back here after studying MVC and Harmonic functions...
@vera_vlog086 жыл бұрын
What about energy surfaces??...can u any explanation about those chemical reactions involving saddle points in their ordinate diagrams
@666ninjafish8 жыл бұрын
thank you
@MrX-il2jt10 күн бұрын
I have to disagree with you on this that it doesn't exist in single variable calculus , from what I remember the point of inflection is analogous to a saddle point, Note : correct me if I am wrong
@md.azmiribneislam68855 жыл бұрын
Awesome discussion ... Really it's praiseworthy ... But I have a question if you don't mind... and the question is - Would you please provide me the information which software are you using for this type of animation ? Waiting eagerly for your reply
@JivanPal7 жыл бұрын
You compare the existence of saddle points in multivariable calc. to their lack of appearance in single variable calc., but what about a function such as f(x) = x³, which has a point of inflection whose tangent has 0 slope? Such functions also appear in multivariable calc, too, such as f(x, y) = x³ + y³.
@fb-gu2er7 жыл бұрын
an inflection point is not the same as a saddle point
@JivanPal7 жыл бұрын
fernando berlanga What about the more specific case of an inflection point at which the derivative is 0, like I mentioned? Is there any difference there?
@anasslyan34906 жыл бұрын
I don't know how to thank you!!!
@deeppatel27273 жыл бұрын
Pringle point!!
@zoechau86664 жыл бұрын
I love 3blue 1brown so much!! :>
@MagnusAnand2 жыл бұрын
This voice looked familiar. It’s Grant from 3blue1brown
@mariakhan38833 жыл бұрын
what is the Definition of saddle point
@arnavrevankar444 Жыл бұрын
Could x^3 (at x=0) be referred to as a "saddle point" for a 2d function? Or does it have another name?
@Oh-lk2qd Жыл бұрын
Point of inflection
@crane8035 Жыл бұрын
grantttttt Sanderson 🤩🤩
@morancium3 жыл бұрын
i want to know in which app he makes the graphs
@eamonnsiocain64542 жыл бұрын
Grant Sanderson of 3Blue1Brown KZbin channel.
@babulsy6460 Жыл бұрын
Is it 3blue1brown?
@surajthapa41606 жыл бұрын
Sir which website or sowtware are you using for graph????plzzz reply
@AnshJhatakia5 жыл бұрын
Suraj Thapa I believe that this is the Grapher app built into Macs.
@AnshJhatakia5 жыл бұрын
It’s very similar to Geogrbra 3D!
@plaustrarius5 жыл бұрын
It's Grant, woohoo!!
@lowpolyduck2 жыл бұрын
Woah 3b hey
@snehamoypatra97864 жыл бұрын
Please someone tell me the name of the instructor
@svaditya28963 жыл бұрын
Grant sanderson
@rishigupta25564 жыл бұрын
What about f(x) = x^3, it's a single variable function but it has f'(x)= 0 at x= 0. Yet at x=0 it's neither a maxima nor minima