Saddle points

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Just because the tangent plane to a multivariable function is flat, it doesn't mean that point is a local minimum or a local maximum. There is a third possibility, new to multivariable calculus, called a "saddle point".

[@rachealmolzahn8932]

I think it would be better if it was called pringle...

[@dreamscapeai7]

Yeah, but the term saddle was coined before a pringle was manufactured

[@ahmedaj2000]

that's what i was thinking too lmao

[@ajmackewicz]

Student on a test: "And there is a pringle point at (0, 0)."
Professor: *visible confusion*

[@YLprime]

pringle engineering

[@shawezonline]

Pringle shape was derived from concept of saddle point

[@mohitkalra9329]

The visualizations are pure gold!

[@ricardovaras4667]

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]

how are you doing

[@kibme5189]

The time has come to honor your promise! In other words it is time for you to pay up buddy.

[@KSM94K]

Okay time to pay now, not sure if you're with us

[@SpeaksYourWord]

@@kibme5189 Lmao he disappeared

[@abhaypratapsingh6067]

u alive my frnd ? pay the bill then

[@damian.gamlath]

I wish Grant could go through and refresh all of Khan's older videos - Grant's stuff is just simply brilliant.

[@robertcharmers3264]

As ever, an adequately comprehensive and clear exposition of a relatively involved topic. Many Thanks.

[@zyzhang1130]

For one variable case it is actually possible for a tangent plane to be flat for neither maximum nor minimum (inflection) 4:36

[@zairaner1489]

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-hz6rk]

Raphael Schmidpeter Yep. And it's called a point of inflexion.

[@nickmilkshake2661]

Agreed

[@surajitdasgupta2540]

You guys are really great

[@LayneSadler]

you missed the word "local"

[@carultch]

That's why the 2nd derivative test is inconclusive, when the determinant of the matrix is zero.

[@ozboomer_au]

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...

[@tahoon2009]

That's a beautiful visualization, thanks :)

[@sankaracharyadutta9408]

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...

[@zairaner1489]

Exactly. Like x^3

[@stephenbeck7222]

Inflection points in single variable generally are not where the first derivative is zero. That’s the difference.

[@venjaminschuster2797]

Khan academy is my new Netflix! Love it! Thank you very very much!

[@Persian771]

awesome what a beautiful graph It makes it easy to understand.

[@giantneuralnetwork]

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.

[@wildertapiasaenz2333]

These graphics are awesome and help so much conceptually, thank you! 🙏

[@234pg786]

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

[@AdityaFingerstyle]

The instructor in this tutorial is not Sal

[@pavanpatel6758]

what is the software, you are using for the graph?

[@TheAcujlGamer]

Python

[@poojamittal4148]

Thank you so much sir I was unable to understand saddle point before. Thank you for teaching me.

[@semih8448]

very good explanation, thanks!

[@clapathy]

such a clear description of the saddle point

[@anhminhtran7436]

Awesome Videos!!! Thanks a lot Khan :))

[@iwtwb8]

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.

[@worldfromhome4033]

Great visualisation

[@sin3divcx]

Great explanation! May i ask you what program you are using?

[@gurleenkaur9601]

Great inituitive video 😊

[@SiddharthSingh-zd7ny]

Very insightful

[@miguelmendoza4274]

What software do you use to do this???

[@mrapter7]

How does one person know so much?

[@pt-ri4ng]

Khan Academy

[@liabraga4641]

3blue1brown actually

[@shivkarj1456]

Both

[@vera_vlog08]

What about energy surfaces??...can u any explanation about those chemical reactions involving saddle points in their ordinate diagrams

[@666ninjafish]

thank you

[@diastema7224]

could you say that saddle point is a point equilibrium between the x and y planes?

[@shreyasarkar4220]

How are plateaus treated in maxima and minima? When are they considered an extrema point?

[@morancium]

i want to know in which app he makes the graphs

[@anasslyan3490]

I don't know how to thank you!!!

[@Quantum_Dots]

3B1B is here!

[@toja8323]

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?

[@arnavrevankar444]

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]

Point of inflection

[@Savvy07]

That's the voice of 3 blue 1 brown

[@ranjeetthorat1318]

y=x3 − 6x2 + 12x − 5
at x=2 => saddle point ...

[@ShokhanBirlikov]

3blue1brown?

[@zoechau8666]

I love 3blue 1brown so much!! :>

[@haraldlindohf4032]

*Cries in inflection point*

[@MayankGoel447]

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

[@surajthapa4160]

Sir which website or sowtware are you using for graph????plzzz reply

[@AnshJhatakia]

Suraj Thapa I believe that this is the Grapher app built into Macs.

[@AnshJhatakia]

It’s very similar to Geogrbra 3D!

[@Troy-ol5fk]

this 3d graphic is cool

[@mariakhan3883]

what is the Definition of saddle point

[@MCERUTUJAPATIL]

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...

[@JivanPal]

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-gu2er]

an inflection point is not the same as a saddle point

[@JivanPal]

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?

[@edward7282]

So basically saddle points have replaced stationary points of inflection (X=0 for stuff like y=x^3) in the 2D world. Interesting

[@photon2724]

they should rename it to 'pringle points'

[@harryloo007]

When you end up coming back here after studying MVC and Harmonic functions...

[@deeppatel2727]

Pringle point!!

[@crane8035]

grantttttt Sanderson 🤩🤩

[@MagnusAnand]

This voice looked familiar. It’s Grant from 3blue1brown

[@snehamoypatra9786]

Please someone tell me the name of the instructor

[@svaditya2896]

Grant sanderson

[@babulsy6460]

Is it 3blue1brown?

[@lavenderblues]

king

[@plaustrarius]

It's Grant, woohoo!!

[@eamonnsiocain6454]

Grant Sanderson of 3Blue1Brown CZcams channel.

[@lowpolyduck]

Woah 3b hey

[@arift.dogan.youtube]

EYER NOKTASI ( evet ebildiğiniz atın üstündeki eyer)

[@md.azmiribneislam6885]

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

[@shubhamchoure8031]

3blue1brown i know

[@imperfect1801.]

Tsu ❤

[@rishigupta2556]

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

[@satanxavier6774]

But this video is about two variable function

[@itSinger]

Are you 3blue1brown guy ?? I know it's ur voice 😳

[@lucasortengren3844]

K

[@Bbb78651]

pringles!

[@NewOne76]

3blue1brown

[@TigaToonsELTiagor]

Science is not about 'y', it's about 'y not'

[@obsidian7133]

You know one thing Mr. Khan.. People like you prove me wrong everytime I believe that God does not exist on earth..

[@YoYo-nt7yf]

3blue1brown